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 Title
 Statistical Shape Analysis on Manifolds with Applications to Planar Contours and Structural Proteomics.
 Creator

Ellingson, Leif A., Patrangenaru, Vic, Mio, Washington, Zhang, Jinfeng, Niu, Xufeng, Department of Statistics, Florida State University
 Abstract/Description

The technological advances in recent years have produced a wealth of intricate digital imaging data that is analyzed effectively using the principles of shape analysis. Such data often lies on either highdimensional or infinitedimensional manifolds. With computing power also now strong enough to handle this data, it is necessary to develop theoreticallysound methodology to perform the analysis in a computationally efficient manner. In this dissertation, we propose approaches of doing so...
Show moreThe technological advances in recent years have produced a wealth of intricate digital imaging data that is analyzed effectively using the principles of shape analysis. Such data often lies on either highdimensional or infinitedimensional manifolds. With computing power also now strong enough to handle this data, it is necessary to develop theoreticallysound methodology to perform the analysis in a computationally efficient manner. In this dissertation, we propose approaches of doing so for planar contours and the threedimensional atomic structures of protein binding sites. First, we adapt Kendall's definition of direct similarity shapes of finite planar configurations to shapes of planar contours under certain regularity conditions and utilize Ziezold's nonparametric view of Frechet mean shapes. The space of direct similarity shapes of regular planar contours is embedded in a space of HilbertSchmidt operators in order to obtain the VeroneseWhitney extrinsic mean shape. For computations, it is necessary to use discrete approximations of both the contours and the embedding. For cases when landmarks are not provided, we propose an automated, randomized landmark selection procedure that is useful for contour matching within a population and is consistent with the underlying asymptotic theory. For inference on the extrinsic mean direct similarity shape, we consider a onesample neighborhood hypothesis test and the use of nonparametric bootstrap to approximate confidence regions. Bandulasiri et al (2008) suggested using extrinsic reflection sizeandshape analysis to study the relationship between the structure and function of protein binding sites. In order to obtain meaningful results for this approach, it is necessary to identify the atoms common to a group of binding sites with similar functions and obtain proper correspondences for these atoms. We explore this problem in depth and propose an algorithm for simultaneously finding the common atoms and their respective correspondences based upon the Iterative Closest Point algorithm. For a benchmark data set, our classification results compare favorably with those of leading established methods. Finally, we discuss current directions in the field of statistics on manifolds, including a computational comparison of intrinsic and extrinsic analysis for various applications and a brief introduction of sample spaces with manifold stratification.
Show less  Date Issued
 2011
 Identifier
 FSU_migr_etd0053
 Format
 Thesis
 Title
 Estimation from Data Representing a Sample of Curves.
 Creator

Auguste, Anna L., Bunea, Florentina, Mason, Patrick, Hollander, Myles, Huﬀer, Fred, Department of Statistics, Florida State University
 Abstract/Description

This dissertation introduces and assesses an algorithm to generate confidence bands for a regression function or a main effect when multiple data sets are available. In particular it proposes to construct confidence bands for different trajectories and then aggregate these to produce an overall confidence band for a mean function. An estimator of the regression function or main effect is also examined. First, nonparametric estimators and confidence bands are formed on each data set separately...
Show moreThis dissertation introduces and assesses an algorithm to generate confidence bands for a regression function or a main effect when multiple data sets are available. In particular it proposes to construct confidence bands for different trajectories and then aggregate these to produce an overall confidence band for a mean function. An estimator of the regression function or main effect is also examined. First, nonparametric estimators and confidence bands are formed on each data set separately. Then each data set is in turn treated as a testing set for aggregating the preliminary results from the remaining data sets. The criterion used for this aggregation is either the least squares (LS) criterion or a BIC type penalized LS criterion. The proposed estimator is the average over data sets of these aggregates. It is thus a weighted sum of the preliminary estimators. The proposed confidence band is the minimum L1 band of all the M aggregate bands when we only have a main effect. In the case where there is some random effect we suggest an adjustment to the confidence band. In this case, the proposed confidence band is the minimum L1 band of all the M adjusted aggregate bands. Desirable asymptotic properties are shown to hold. A simulation study examines the performance of each technique relative to several alternate methods and theoretical benchmarks. An application to seismic data is conducted.
Show less  Date Issued
 2006
 Identifier
 FSU_migr_etd0286
 Format
 Thesis
 Title
 TimeVarying Coefficient Models with ARMAGARCH Structures for Longitudinal Data Analysis.
 Creator

Zhao, Haiyan, Niu, Xufeng, Huﬀer, Fred, Nolder, Craig, McGee, Dan, Department of Statistics, Florida State University
 Abstract/Description

The motivation of my research comes from the analysis of the Framingham Heart Study (FHS) data. The FHS is a long term prospective study of cardiovascular disease in the community of Framingham, Massachusetts. The study began in 1948 and 5,209 subjects were initially enrolled. Examinations were given biennially to the study participants and their status associated with the occurrence of disease was recorded. In this dissertation, the event we are interested in is the incidence of the coronary...
Show moreThe motivation of my research comes from the analysis of the Framingham Heart Study (FHS) data. The FHS is a long term prospective study of cardiovascular disease in the community of Framingham, Massachusetts. The study began in 1948 and 5,209 subjects were initially enrolled. Examinations were given biennially to the study participants and their status associated with the occurrence of disease was recorded. In this dissertation, the event we are interested in is the incidence of the coronary heart disease (CHD). Covariates considered include sex, age, cigarettes per day (CSM), serum cholesterol (SCL), systolic blood pressure (SBP) and body mass index (BMI, weight in kilograms/height in meters squared). Statistical literature review indicates that effects of the covariates on Cardiovascular disease or death caused by all possible diseases in the Framingham study change over time. For example, the effect of SCL on Cardiovascular disease decreases linearly over time. In this study, I would like to examine the timevarying effects of the risk factors on CHD incidence. Timevarying coefficient models with ARMAGARCH structure are developed in this research. The maximum likelihood and the marginal likelihood methods are used to estimate the parameters in the proposed models. Since highdimensional integrals are involved in the calculations of the marginal likelihood, the Laplace approximation is employed in this study. Simulation studies are conducted to evaluate the performance of these two estimation methods based on our proposed models. The KullbackLeibler (KL) divergence and the root mean square error are employed in the simulation studies to compare the results obtained from different methods. Simulation results show that the marginal likelihood approach gives more accurate parameter estimates, but is more computationally intensive. Following the simulation study, our proposed models are applied to the Framingham Heart Study to investigate the timevarying effects of covariates with respect to CHD incidence. To specify the timeseries structures of the effects of risk factors, the Bayesian Information Criterion (BIC) is used for model selection. Our study shows that the relationship between CHD and risk factors changes over time. For males, there is an obviously decreasing linear trend for age effect, which implies that the age effect on CHD is less significant for elder patients than younger patients. The effect of CSM stays almost the same in the first 30 years and decreases thereafter. There are slightly decreasing linear trends for both effects of SBP and BMI. Furthermore, the coefficients of SBP are mostly positive over time, i.e., patients with higher SBP are more likely developing CHD as expected. For females, there is also an obviously decreasing linear trend for age effect, while the effects of SBP and BMI on CHD are mostly positive and do not change too much over time.
Show less  Date Issued
 2010
 Identifier
 FSU_migr_etd0527
 Format
 Thesis
 Title
 Individual PatientLevel Data MetaAnalysis: A Comparison of Methods for the Diverse Populations Collaboration Data Set.
 Creator

Dutton, Matthew Thomas, McGee, Daniel, Becker, Betsy, Niu, Xufeng, Zhang, Jinfeng, Department of Statistics, Florida State University
 Abstract/Description

DerSimonian and Laird define metaanalysis as "the statistical analysis of a collection of analytic results for the purpose of integrating their findings. One alternative to classical metaanalytic approaches in known as Individual PatientLevel Data, or IPD, metaanalysis. Rather than depending on summary statistics calculated for individual studies, IPD metaanalysis analyzes the complete data from all included studies. Two potential approaches to incorporating IPD data into the meta...
Show moreDerSimonian and Laird define metaanalysis as "the statistical analysis of a collection of analytic results for the purpose of integrating their findings. One alternative to classical metaanalytic approaches in known as Individual PatientLevel Data, or IPD, metaanalysis. Rather than depending on summary statistics calculated for individual studies, IPD metaanalysis analyzes the complete data from all included studies. Two potential approaches to incorporating IPD data into the metaanalytic framework are investigated. A twostage analysis is first conducted, in which individual models are fit for each study and summarized using classical metaanalysis procedures. Secondly, a onestage approach that singularly models the data and summarizes the information across studies is investigated. Data from the Diverse Populations Collaboration data set are used to investigate the differences between these two methods in a specific example. The bootstrap procedure is used to determine if the two methods produce statistically different results in the DPC example. Finally, a simulation study is conducted to investigate the accuracy of each method in given scenarios.
Show less  Date Issued
 2011
 Identifier
 FSU_migr_etd0620
 Format
 Thesis
 Title
 A Comparison of Estimators in Hierarchical Linear Modeling: Restricted Maximum Likelihood versus Bootstrap via Minimum Norm Quadratic Unbiased Estimators.
 Creator

Delpish, Ayesha Nneka, Niu, XuFeng, Tate, Richard L., Huﬀer, Fred W., Zahn, Douglas, Department of Statistics, Florida State University
 Abstract/Description

The purpose of the study was to investigate the relative performance of two estimation procedures, the restricted maximum likelihood (REML) and the bootstrap via MINQUE, for a twolevel hierarchical linear model under a variety of conditions. Specific focus lay on observing whether the bootstrap via MINQUE procedure offered improved accuracy in the estimation of the model parameters and their standard errors in situations where normality may not be guaranteed. Through Monte Carlo simulations,...
Show moreThe purpose of the study was to investigate the relative performance of two estimation procedures, the restricted maximum likelihood (REML) and the bootstrap via MINQUE, for a twolevel hierarchical linear model under a variety of conditions. Specific focus lay on observing whether the bootstrap via MINQUE procedure offered improved accuracy in the estimation of the model parameters and their standard errors in situations where normality may not be guaranteed. Through Monte Carlo simulations, the importance of this assumption for the accuracy of multilevel parameter estimates and their standard errors was assessed using the accuracy index of relative bias and by observing the coverage percentages of 95% confidence intervals constructed for both estimation procedures. The study systematically varied the number of groups at level2 (30 versus 100), the size of the intraclass correlation (0.01 versus 0.20) and the distribution of the observations (normal versus chisquared with 1 degree of freedom). The number of groups and intraclass correlation factors produced effects consistent with those previously reported—as the number of groups increased, the bias in the parameter estimates decreased, with a more significant effect observed for those estimates obtained via REML. High levels of the intraclass correlation also led to a decrease in the efficiency of parameter estimation under both methods. Study results show that while both the restricted maximum likelihood and the bootstrap via MINQUE estimates of the fixed effects were accurate, the efficiency of the estimates was affected by the distribution of errors with the bootstrap via MINQUE procedure outperforming the REML. Both procedures produced less efficient estimators under the chisquared distribution, particularly for the variancecovariance component estimates.
Show less  Date Issued
 2006
 Identifier
 FSU_migr_etd0771
 Format
 Thesis
 Title
 Minimax Tests for Nonparametric Alternatives with Applications to High Frequency Data.
 Creator

Yu, Han, Song, KaiSheng, Professor, Jack Quine, Professor, Fred Huﬀer, Professor, Dan McGee, Department of Statistics, Florida State University
 Abstract/Description

We present a general methodology for developing an asymptotically distributionfree, asymptotic minimax tests. The tests are constructed via a nonparametric densityquantile function and the limiting distribution is derived by a martingale approach. The procedure can be viewed as a novel parametric extension of the classical parametric likelihood ratio test. The proposed tests are shown to be omnibus within an extremely large class of nonparametric global alternatives characterized by simple...
Show moreWe present a general methodology for developing an asymptotically distributionfree, asymptotic minimax tests. The tests are constructed via a nonparametric densityquantile function and the limiting distribution is derived by a martingale approach. The procedure can be viewed as a novel parametric extension of the classical parametric likelihood ratio test. The proposed tests are shown to be omnibus within an extremely large class of nonparametric global alternatives characterized by simple conditions. Furthermore, we establish that the proposed tests provide better minimax distinguishability. The tests have much greater power for detecting highfrequency nonparametric alternatives than the existing classical tests such as KolmogorovSmirnov and Cramervon Mises tests. The good performance of the proposed tests is demonstrated by Monte Carlo simulations and applications in High Energy Physics.
Show less  Date Issued
 2006
 Identifier
 FSU_migr_etd0796
 Format
 Thesis
 Title
 Inference for Semiparametric TimeVarying Covariate Effect Relative Risk Regression Models.
 Creator

Ye, Gang, McKeague, Ian W., Wang, Xiaoming, Huffer, Fred W., Song, KaiSheng, Department of Statistics, Florida State University
 Abstract/Description

A major interest of survival analysis is to assess covariate effects on survival via appropriate conditional hazard function regression models. The Cox proportional hazards model, which assumes an exponential form for the relative risk, has been a popular choice. However, other regression forms such as Aalen's additive risk model may be more appropriate in some applications. In addition, covariate effects may depend on time, which can not be reflected by a Cox proportional hazards model. In...
Show moreA major interest of survival analysis is to assess covariate effects on survival via appropriate conditional hazard function regression models. The Cox proportional hazards model, which assumes an exponential form for the relative risk, has been a popular choice. However, other regression forms such as Aalen's additive risk model may be more appropriate in some applications. In addition, covariate effects may depend on time, which can not be reflected by a Cox proportional hazards model. In this dissertation, we study a class of timevarying covariate effect regression models in which the link function (relative risk function) is a twice continuously differentiable and prespecified, but otherwise general given function. This is a natural extension of the PrenticeSelf model, in which the link function is general but covariate effects are modelled to be time invariant. In the first part of the dissertation, we focus on estimating the cumulative or integrated covariate effects. The standard martingale approach based on counting processes is utilized to derive a likelihoodbased iterating equation. An estimator for the cumulative covariate effect that is generated from the iterating equation is shown to be ¡Ìnconsistent. Asymptotic normality of the estimator is also demonstrated. Another aspect of the dissertation is to investigate a new test for the above timevarying covariate effect regression model and study consistency of the test based on martingale residuals. For Aalen's additive risk model, we introduce a test statistic based on the HufferMcKeague weightedleastsquares estimator and show its consistency against some alternatives. An alternative way to construct a test statistic based on Bayesian Bootstrap simulation is introduced. An application to real lifetime data will be presented.
Show less  Date Issued
 2005
 Identifier
 FSU_migr_etd0949
 Format
 Thesis
 Title
 Age Effects in the Extinction of Planktonic Foraminifera: A New Look at Van Valen's Red Queen Hypothesis.
 Creator

Wiltshire, Jelani, Huﬀer, Fred, Parker, William, Chicken, Eric, Sinha, Debajyoti, Department of Statistics, Florida State University
 Abstract/Description

Van Valen's Red Queen hypothesis states that within a homogeneous taxonomic group the age is statistically independent of the rate of extinction. The case of the Red Queen hypothesis being addressed here is when the homogeneous taxonomic group is a group of similar species. Since Van Valen's work, various statistical approaches have been used to address the relationship between taxon duration (age) and the rate of extinction. Some of the more recent approaches to this problem using Planktonic...
Show moreVan Valen's Red Queen hypothesis states that within a homogeneous taxonomic group the age is statistically independent of the rate of extinction. The case of the Red Queen hypothesis being addressed here is when the homogeneous taxonomic group is a group of similar species. Since Van Valen's work, various statistical approaches have been used to address the relationship between taxon duration (age) and the rate of extinction. Some of the more recent approaches to this problem using Planktonic Foraminifera (Foram) extinction data include Weibull and Exponential modeling (Parker and Arnold, 1997), and Cox proportional hazards modeling (Doran et al. 2004,2006). I propose a general class of test statistics that can be used to test for the effect of age on extinction. These test statistics allow for a varying background rate of extinction and attempt to remove the effects of other covariates when assessing the effect of age on extinction. No model is assumed for the covariate effects. Instead I control for covariate effects by pairing or grouping together similar species. I use simulated data sets to compare the power of the statistics. In applying the test statistics to the Foram data, I have found age to have a positive effect on extinction.
Show less  Date Issued
 2010
 Identifier
 FSU_migr_etd0952
 Format
 Thesis
 Title
 Transformation Models for Survival Data Analysis and Applications.
 Creator

Liu, Yang, Niu, XuFeng, Lloyd, Donald, McGee, Dan, Sinha, Debajyoti, Department of Statistics, Florida State University
 Abstract/Description

It is often assumed that all uncensored subjects will eventually experience the event of interest in standard survival models. However, in some situations when the event considered is not death, it will never occur for a proportion of subjects. Survival models with a cure fraction are becoming popular in analyzing this type of study. We propose a generalized transformation model motivated by Zeng et al's (2006) transformed proportional time cure model. In our proposed model, fractional...
Show moreIt is often assumed that all uncensored subjects will eventually experience the event of interest in standard survival models. However, in some situations when the event considered is not death, it will never occur for a proportion of subjects. Survival models with a cure fraction are becoming popular in analyzing this type of study. We propose a generalized transformation model motivated by Zeng et al's (2006) transformed proportional time cure model. In our proposed model, fractional polynomials are used instead of the simple linear combination of the covariates. The proposed models give us more flexibility without loosing any good properties of the original model, such as asymptotic consistency and asymptotic normality of the regression coefficients. The proposed model will better fit the data where the relationship between a response variable and covariates is nonlinear. We also provide a power selection procedure based on the likelihood function. A simulation study is carried out to show the accuracy of the proposed power selection procedure. The proposed models are applied to coronary heart disease and cancer related medical data from both observational cohort studies and clinical trials
Show less  Date Issued
 2009
 Identifier
 FSU_migr_etd1155
 Format
 Thesis
 Title
 Ultrafast Lattice Dynamics in Metal Thin Films and NanoParticles.
 Creator

Wang, Xuan, Cao, Jim, Yang, Wei, Bonesteel, Nicholas, Riley, Mark, Xiong, Peng, Department of Physics, Florida State University
 Abstract/Description

This thesis presents the new development of the 3rd generation femtosecond diffractometer (FED) in Professor Jim Cao's group and its application to study ultrafast structural dynamics of solid state materials. The 3rd generation FED prevails its former type and other similar FED instruments by a DC electron gun that can generate much higher energy electron pulses, and a more efficient imaging system. This combination together with miscellaneous improvements significantly boosts the signalto...
Show moreThis thesis presents the new development of the 3rd generation femtosecond diffractometer (FED) in Professor Jim Cao's group and its application to study ultrafast structural dynamics of solid state materials. The 3rd generation FED prevails its former type and other similar FED instruments by a DC electron gun that can generate much higher energy electron pulses, and a more efficient imaging system. This combination together with miscellaneous improvements significantly boosts the signaltonoise ratio and thus enables us to study more complex solid state materials. Two main thrusts are discussed in details in this thesis. The first one is the dynamics of coherent phonon generation by ultrafast heating in gold thin film and nanoparticles, which emphasizes the electronic thermal stress. The other one is the ultrafast dynamics in Nickel, which shows that the mutual interactions among lattice, spin and electron subsystems can significantly alter the ultrafast lattice dynamics. In these studies, we exploit the advantage of FED instrument as an ideal tool that can directly and simultaneously monitor the coherent and random motion of lattice.
Show less  Date Issued
 2010
 Identifier
 FSU_migr_etd1247
 Format
 Thesis
 Title
 Association Models for Clustered Data with Binary and Continuous Responses.
 Creator

Lin, Lanjia, Sinha, Debajyoti, Hurt, Myra, Lipsitz, Stuart R., McGee, Daniel, Department of Statistics, Florida State University
 Abstract/Description

This dissertation develops novel single random effect models as well as bivariate correlated random effects model for clustered data with bivariate mixed responses. Logit and identity link functions are used for the binary and continuous responses. For the ease of interpretation of the regression effects, random effect of the binary response has bridge distribution so that the marginal model of mean of the binary response after integrating out the random effect preserves logistic form. And...
Show moreThis dissertation develops novel single random effect models as well as bivariate correlated random effects model for clustered data with bivariate mixed responses. Logit and identity link functions are used for the binary and continuous responses. For the ease of interpretation of the regression effects, random effect of the binary response has bridge distribution so that the marginal model of mean of the binary response after integrating out the random effect preserves logistic form. And the marginal regression function of the continuous response preserves linear form. Withincluster and withinsubject associations could be measured by our proposed models. For the bivariate correlated random effects model, we illustrate how different levels of the association between two random effects induce different Kendall's tau values for association between the binary and continuous responses from the same cluster. Fully parametric and semiparametric Bayesian methods as well as maximum likelihood method are illustrated for model analysis. In the semiparametric Bayesian model, normality assumption of the regression error for the continuous response is relaxed by using a nonparametric Dirichlet Process prior. Robustness of the bivariate correlated random effects model using ML method to misspecifications of regression function as well as random effect distribution is investigated by simulation studies. The Bayesian and likelihood methods are applied to a developmental toxicity study of ethylene glycol in mice.
Show less  Date Issued
 2009
 Identifier
 FSU_migr_etd1330
 Format
 Thesis
 Title
 Multistate Intensity Model with ARGARCH Random Effect for Corporate Credit Rating Transition Analysis.
 Creator

Li, Zhi, Niu, Xufeng, Huﬀer, Fred, Kercheval, Alec, Wu, Wei, Department of Statistics, Florida State University
 Abstract/Description

This thesis presents a stochastic process and time series study on corporate credit rating and market implied rating transitions. By extending an existing model, this paper incorporates the generalized autoregressive conditional heteroscedastic (GARCH) random effects to capture volatility changes in the instantaneous transition rates. The GARCH model is a crucial part in financial research since its ability to model volatility changes gives the market practitioners flexibility to build more...
Show moreThis thesis presents a stochastic process and time series study on corporate credit rating and market implied rating transitions. By extending an existing model, this paper incorporates the generalized autoregressive conditional heteroscedastic (GARCH) random effects to capture volatility changes in the instantaneous transition rates. The GARCH model is a crucial part in financial research since its ability to model volatility changes gives the market practitioners flexibility to build more accurate models on high frequency financial data. The corporate rating transition modeling was historically dealing with low frequency data which did not have the need to specify the volatility. However, the newly published Moody's market implied ratings are exhibiting much higher transition frequencies. Therefore, we feel that it is necessary to capture the volatility component and make extensions to existing models to reflect this fact. The theoretical model specification and estimation details are discussed thoroughly in this dissertation. The performance of our models is studied on several simulated data sets and compared to the original model. Finally, the models are applied to both Moody's issuer rating and market implied rating transition data as an application.
Show less  Date Issued
 2010
 Identifier
 FSU_migr_etd1426
 Format
 Thesis
 Title
 The Effect of Risk Factors on Coronary Heart Disease: An AgeRelevant Multivariate Meta Analysis.
 Creator

Li, Yan, McGee, Dan, She, Yiyuan, Eberstein, Ike, Niu, Xufeng, Department of Statistics, Florida State University
 Abstract/Description

The importance of major risk factors, such as hypertension, total cholesterol, body mass index, diabetes, smoking, for predicting incidence and mortality of Coronary Heart Disease (CHD) is well known. In light of the fact that age is also a major risk factor for CHD death, a natural question is whether the risk effects on CHD change with age. This thesis focuses on examining the interaction between age and risk factors using data from multiple studies containing differing age ranges. The aim...
Show moreThe importance of major risk factors, such as hypertension, total cholesterol, body mass index, diabetes, smoking, for predicting incidence and mortality of Coronary Heart Disease (CHD) is well known. In light of the fact that age is also a major risk factor for CHD death, a natural question is whether the risk effects on CHD change with age. This thesis focuses on examining the interaction between age and risk factors using data from multiple studies containing differing age ranges. The aim of my research is to use statistical methods to determine whether we can combine these diverse results to obtain an overall summary, using which one can find how the risk effects on CHD death change with age. One intuitive approach is to use classical meta analysis based on generalized linear models. More specifically, one can fit a logistic model with CHD death as response and age, a risk factor and their interaction as covariates for each of the studies, and conduct meta analysis on every set of three coefficients in the multivariate setting to obtain 'synthesized' coefficients. Another aspect of the thesis is a new method, meta analysis with respect to curves that goes beyond linear models. The basic idea is that one can choose the same spline with the same knots on covariates, say age and systolic blood pressure (SBP), for all the studies to ensure common basis functions. The knotbased tensor product basis coefficients obtained from penalized logistic regression can be used for multivariate meta analysis. Using the common basis functions and the 'synthesized' knotbased basis coefficients from meta analysis, a twodimensional smooth surface on the ageSBP domain is estimated. By cutting through the smooth surface along two axes, the resulting slices show how the risk effect on CHD death change at an arbitrary age as well as how the age effect on CHD death change at an arbitrary SBP value. The application to multiple studies will be presented.
Show less  Date Issued
 2010
 Identifier
 FSU_migr_etd1428
 Format
 Thesis
 Title
 Flexible Additive Risk Models Using Piecewise Constant Hazard Functions.
 Creator

Uhm, Daiho, Huﬀer, Fred W., Kercheval, Alec, McGee, Dan, Niu, Xufeng, Department of Statistics, Florida State University
 Abstract/Description

We study a weighted least squares (WLS) estimator for Aalen's additive risk model which allows for a very flexible handling of covariates. We divide the followup period into intervals and assume a constant hazard rate in each interval. The model is motivated as a piecewise approximation of a hazard function composed of three parts: arbitrary nonparametric functions for some covariate effects, smoothly varying functions for others, and known (or constant) functions for yet others. The...
Show moreWe study a weighted least squares (WLS) estimator for Aalen's additive risk model which allows for a very flexible handling of covariates. We divide the followup period into intervals and assume a constant hazard rate in each interval. The model is motivated as a piecewise approximation of a hazard function composed of three parts: arbitrary nonparametric functions for some covariate effects, smoothly varying functions for others, and known (or constant) functions for yet others. The proposed estimator is an extension of the grouped data version of the HufferMcKeague estimator (1991). Our estimator may also be regarded as a piecewise constant analog of the semiparametric estimates of McKeague & Sasieni (1994), and Lin & Ying (1994). By using a fairly large number of intervals, we should get an essentially semiparametric model similar to the McKeagueSasieni and LinYing approaches. For our model, since the number of parameters is finite (although large), conventional approaches (such as maximum likelihood) are easy to formulate and implement. The approach is illustrated by simulations, and is applied to data from the Framingham heart study.
Show less  Date Issued
 2007
 Identifier
 FSU_migr_etd1464
 Format
 Thesis
 Title
 A Class of MixedDistribution Models with Applications in Financial Data Analysis.
 Creator

Tang, Anqi, Niu, Xufeng, Cheng, Yingmei, Wu, Wei, Huﬀer, Fred, Department of Statistics, Florida State University
 Abstract/Description

Statisticians often encounter data in the form of a combination of discrete and continuous outcomes. A special case is zeroinflated longitudinal data where the response variable has a large portion of zeros. These data exhibit correlation because observations are obtained on the same subjects over time. In this dissertation, we propose a twopart mixed distribution model to model zeroinflated longitudinal data. The first part of the model is a logistic regression model that models the...
Show moreStatisticians often encounter data in the form of a combination of discrete and continuous outcomes. A special case is zeroinflated longitudinal data where the response variable has a large portion of zeros. These data exhibit correlation because observations are obtained on the same subjects over time. In this dissertation, we propose a twopart mixed distribution model to model zeroinflated longitudinal data. The first part of the model is a logistic regression model that models the probability of nonzero response; the other part is a linear model that models the mean response given that the outcomes are not zeros. Random effects with AR(1) covariance structure are introduced into both parts of the model to allow serial correlation and subject specific effect. Estimating the twopart model is challenging because of high dimensional integration necessary to obtain the maximum likelihood estimates. We propose a Monte Carlo EM algorithm for estimating the maximum likelihood estimates of parameters. Through simulation study, we demonstrate the good performance of the MCEM method in parameter and standard error estimation. To illustrate, we apply the twopart model with correlated random effects and the model with autoregressive random effects to executive compensation data to investigate potential determinants of CEO stock option grants.
Show less  Date Issued
 2011
 Identifier
 FSU_migr_etd1710
 Format
 Thesis
 Title
 A Method for Finding the Nadir of NonMonotonic Relationships.
 Creator

Tan, Fei, McGee, Daniel, Lloyd, Donald, Huﬀer, Fred, Niu, Xufeng, Dutton, Gareth, Department of Statistics, Florida State University
 Abstract/Description

Different methods have been proposed to model the Jshaped or Ushaped relationship between a risk factor and mortality so that the optimal riskfactor value (nadir) associated with the lowest mortality can be estimated. The basic model considered is the Cox Proportional Hazards model. Current methods include a quadratic method, a method with transformation, fractional polynomials, a change point method and fixedknot spline regression. A quadratic method contains both the linear and the...
Show moreDifferent methods have been proposed to model the Jshaped or Ushaped relationship between a risk factor and mortality so that the optimal riskfactor value (nadir) associated with the lowest mortality can be estimated. The basic model considered is the Cox Proportional Hazards model. Current methods include a quadratic method, a method with transformation, fractional polynomials, a change point method and fixedknot spline regression. A quadratic method contains both the linear and the quadratic term of the risk factor, it is simple but often it generates unrealistic nadir estimates. The transformation method converts the original risk factor so that after transformation it has a Normal distribution, but this may not work when there is no good transformation to normality. Fractional polynomials are an extended class of regular polynomials that applies negative and fractional powers to the risk factor. Compared with the quadratic method or the transformation method it does not always have a good model interpretation and inferences about it do not incorporate the uncertainty coming from preselection of powers and degree. A change point method models the prognostic index using two pieces of upward quadratic functions that meet at their common nadir. This method assumes the knot and the nadir are the same, which is not always true. Fixedknot spline regression has also been used to model nonlinear prognostic indices. But its inference does not account for variation arising from knot selections. Here we consider spline regressions with free knots, a natural generalization of the quadratic, the change point and the fixedknot spline method. They can be applied to risk factors that do not have a good transformation to normality as well as keep intuitive model interpretations. Asymptotic normality and consistency of the maximum partial likelihood estimators are established under certain condition. When the condition is not satisfied simulations are used to explore asymptotic properties. The new method is motivated by and applied to the nadir estimation in nonmonotonic relationships between BMI (body mass index) and allcause mortality. Its performance is compared with that of existing methods, adopting criteria of nadir estimation ability and goodness of fit.
Show less  Date Issued
 2007
 Identifier
 FSU_migr_etd1719
 Format
 Thesis
 Title
 Logistic Regression, Measures of Explained Variation, and the Base Rate Problem.
 Creator

Sharma, Dinesh R., McGee, Daniel L., Hurt, Myra, Niu, XuFeng, Chicken, Eric, Department of Statistics, Florida State University
 Abstract/Description

One of the desirable properties of the coefficient of determinant (R2 measure) is that its values for different models should be comparable whether the models differ in one or more predictors, or in the dependent variable, or whether the models are specified as being different for different subsets of a dataset. This allows researchers to compare adequacy of models across subgroups of the population or models with different but related dependent variables. However, the various analogs of the...
Show moreOne of the desirable properties of the coefficient of determinant (R2 measure) is that its values for different models should be comparable whether the models differ in one or more predictors, or in the dependent variable, or whether the models are specified as being different for different subsets of a dataset. This allows researchers to compare adequacy of models across subgroups of the population or models with different but related dependent variables. However, the various analogs of the R2 measure used for logistic regression analysis are highly sensitive to the base rate (proportion of successes in the sample) and thus do not possess this property. An R2 measure sensitive to the base rate is not suitable to comparison for the same or different model on different datasets, different subsets of a dataset or different but related dependent variables. We evaluated 14 R2 measures that have been suggested or might be useful to measure the explained variation in the logistic regression models based on three criteria 1) intuitively reasonable interpret ability; 2) numerical consistency with the Rho2 of underlying model, and 3) the base rate sensitivity. We carried out a Monte Carlo Simulation study to examine the numerical consistency and the base rate dependency of the various R2 measures for logistic regression analysis. We found all of the parametric R2 measures to be substantially sensitive to the base rate. The magnitude of the base rate sensitivity of these measures tends to be further influenced by the rho2 of the underlying model. None of the measures considered in our study are found to perform equally well in all of the three evaluation criteria used. While R2L stands out for its intuitively reasonable interpretability as a measures of explained variation as well as its independence from the base rate, it appears to severely underestimate the underlying rho2. We found R2CS to be numerically most consistent with the underlying Rho2, with R2N its nearest competitor. In addition, the base rate sensitivity of these two measures appears to be very close to that of the R2L, the most base rate invariant parametric R2 measure. Therefore, we suggest to use R2CS and R2N for logistic regression modeling, specially when it is reasonable to believe that a underlying latent variable exists. However, when the latent variable does not exit, comparability with theunderlying rho2 is not an issue and R2L might be a better choice over all the R2 measures.
Show less  Date Issued
 2006
 Identifier
 FSU_migr_etd1789
 Format
 Thesis
 Title
 Interrelating of Longitudinal Processes: An Empirical Example.
 Creator

RoyalThomas, Tamika Y. N., McGee, Daniel, Levenson, Cathy, Sinha, Debajyoti, Osmond, Clive, Niu, Xufeng, Department of Statistics, Florida State University
 Abstract/Description

The Barker Hypothesis states that maternal and `in utero' attributes during pregnancy affects a child's cardiovascular health throughout life. We present an analysis of a unique longitudinal dataset from Jamaica that consists of three longitudinal processes: (i) Maternal longitudinal process Blood pressure and anthropometric measurements at seven timepoints on the mother during pregnancy. (ii) In Utero measurements  Ultrasound measurements of the fetus taken at six timepoints during...
Show moreThe Barker Hypothesis states that maternal and `in utero' attributes during pregnancy affects a child's cardiovascular health throughout life. We present an analysis of a unique longitudinal dataset from Jamaica that consists of three longitudinal processes: (i) Maternal longitudinal process Blood pressure and anthropometric measurements at seven timepoints on the mother during pregnancy. (ii) In Utero measurements  Ultrasound measurements of the fetus taken at six timepoints during pregnancy. (iii) Birth to present process  Children's anthropometric and blood pressure measurements at 24 timepoints from birth to 14 years. A comprehensive analysis of the interrelationship of these three longitudinal processes is presented using joint modeling for multivariate longitudinal profiles. We propose a new methodology of examining child's cardiovascular risk by extending a current view of likelihood estimation. Joint modeling of multivariate longitudinal profiles is done and the extension of the traditional likelihood method is utilized in this paper and compared to the maximum likelihood estimates. Our main goal is to examine whether the process in mothers predicts fetal development which in turn predicts the future cardiovascular health of the children. One of the difficulties with `in utero' and early childhood data is that certain variables are highly correlated and so using dimension reduction techniques are quite applicable in this scenario. Principal component analysis (PCA) is utilized in creating a smaller dimension of uncorrelated data which is then utilized in a longitudinal analysis setting. These principal components are then utilized in an optimal linear mixed model for longitudinal data which indicates that in utero and early childhood attributes predicts the future cardiovascular health of the children. This dissertation has added a body of knowledge to developmental origins of adult diseases and has supplied some significant results while utilizing a rich diversity of statistical methodologies.
Show less  Date Issued
 2011
 Identifier
 FSU_migr_etd1792
 Format
 Thesis
 Title
 Optimal Linear Representations of Images under Diverse Criteria.
 Creator

Rubinshtein, Evgenia, Srivastava, Anuj, Liu, Xiuwen, Huﬀer, Fred, Chicken, Eric, Department of Statistics, Florida State University
 Abstract/Description

Image analysis often requires dimension reduction before statistical analysis, in order to apply sophisticated procedures. Motivated by eventual applications, a variety of criteria have been proposed: reconstruction error, class separation, nonGaussianity using kurtosis, sparseness, mutual information, recognition of objects, and their combinations. Although some criteria have analytical solutions, the remaining ones require numerical approaches. We present geometric tools for finding linear...
Show moreImage analysis often requires dimension reduction before statistical analysis, in order to apply sophisticated procedures. Motivated by eventual applications, a variety of criteria have been proposed: reconstruction error, class separation, nonGaussianity using kurtosis, sparseness, mutual information, recognition of objects, and their combinations. Although some criteria have analytical solutions, the remaining ones require numerical approaches. We present geometric tools for finding linear projections that optimize a given criterion for a given data set. The main idea is to formulate a problem of optimization on a Grassmann or a Stiefel manifold, and to use differential geometry of the underlying space to construct optimization algorithms. Purely deterministic updates lead to local solutions, and addition of random components allows for stochastic gradient searches that eventually lead to global solutions. We demonstrate these results using several image datasets, including natural images and facial images.
Show less  Date Issued
 2006
 Identifier
 FSU_migr_etd1926
 Format
 Thesis
 Title
 Impact of Missing Data on Building Prognostic Models and Summarizing Models Across Studies.
 Creator

Munshi, Mahtab R., McGee, Daniel, Eberstein, Isaac, Hollander, Myles, Niu, Xufeng, Chattopadhyay, Somesh, Department of Statistics, Florida State University
 Abstract/Description

We examine the impact of missing data in two settings, the development of prognostic models and the addition of new risk factors to existing risk functions. Most statistical software presently available perform complete case analysis, wherein only participants with known values for all of the characteristics being analyzed are included in model development. Missing data also impacts the summarization of evidence amongst multiple studies using metaanalytic techniques. As we progress in...
Show moreWe examine the impact of missing data in two settings, the development of prognostic models and the addition of new risk factors to existing risk functions. Most statistical software presently available perform complete case analysis, wherein only participants with known values for all of the characteristics being analyzed are included in model development. Missing data also impacts the summarization of evidence amongst multiple studies using metaanalytic techniques. As we progress in medical research, new covariates become available for studying various outcomes. While we want to investigate the influence of new factors on the outcome, we also do not want to discard the historical datasets that do not have information about these markers. Our research plan is to investigate different methods to estimate parameters for a model when some of the covariates are missing. These methods include likelihood based inference for the studylevel coefficients and likelihood based inference for the logistic model on the personlevel data. We compare the results from our methods to the corresponding results from complete case analysis. We focus our empirical investigation on a historical example, the addition of high density lipoproteins to existing equations for predicting death due to coronary heart disease. We verify our methods through simulation studies on this example.
Show less  Date Issued
 2005
 Identifier
 FSU_migr_etd2191
 Format
 Thesis
 Title
 Spatiotemporal Bayesian Hierarchical Models, with Application to Birth Outcomes.
 Creator

Norton, Jonathan D. (Jonathan David), Niu, Xufeng, Eberstein, Isaac, Huﬀer, Fred, McGee, Daniel, Department of Statistics, Florida State University
 Abstract/Description

A class of hierarchical Bayesian models is introduced for adverse birth outcomes such as preterm birth, which are assumed to follow a conditional binomial distribution. The logodds of an adverse outcome in a particular county, logit(p(i)), follows a linear model which includes observed covariates and normallydistributed random effects. Spatial dependence between neighboring regions is allowed for by including an intrinsic autoregressive (IAR) prior or an IAR convolution prior in the linear...
Show moreA class of hierarchical Bayesian models is introduced for adverse birth outcomes such as preterm birth, which are assumed to follow a conditional binomial distribution. The logodds of an adverse outcome in a particular county, logit(p(i)), follows a linear model which includes observed covariates and normallydistributed random effects. Spatial dependence between neighboring regions is allowed for by including an intrinsic autoregressive (IAR) prior or an IAR convolution prior in the linear predictor. Temporal dependence is incorporated by including a temporal IAR term also. It is shown that the variance parameters underlying these random effects (IAR, convolution, convolution plus temporal IAR) are identifiable. The same results are also shown to hold when the IAR is replaced by a conditional autoregressive (CAR) model. Furthermore, properties of the CAR parameter ρ are explored. The Deviance Information Criterion (DIC) is considered as a way to compare spatial hierarchical models. Simulations are performed to test whether the DIC can identify whether binomial outcomes come from an IAR, an IAR convolution, or independent normal deviates. Having established the theoretical foundations of the class of models and validated the DIC as a means of comparing models, we examine preterm birth and low birth weight counts in the state of Arkansas from 1994 to 2005. We find that preterm birth and low birth weight have different spatial patterns of risk, and that rates of low birth weight can be fit with a strikingly simple model that includes a constant spatial effect for all periods, a linear trend, and three covariates. It is also found that the risks of each outcome are increasing over time, even with adjustment for covariates.
Show less  Date Issued
 2008
 Identifier
 FSU_migr_etd2523
 Format
 Thesis
 Title
 A Bayesian MRF Framework for Labeling Terrain Using Hyperspectral Imaging.
 Creator

Neher, Robert E., Srivastava, Anuj, Liu, Xiuwen, Huffer, Fred, Wegkamp, Marten, Department of Statistics, Florida State University
 Abstract/Description

We explore the nonGaussianity of hyperspectral data and present probability models that capture variability of hyperspectral images. In particular, we present a nonparametric probability distribution that models the distribution of the hyperspectral data after reducing the dimension of the data via either principal components or Fisher's discriminant analysis. We also explore the directional differences in observed images and present two parametric distributions, the generalized Laplacian...
Show moreWe explore the nonGaussianity of hyperspectral data and present probability models that capture variability of hyperspectral images. In particular, we present a nonparametric probability distribution that models the distribution of the hyperspectral data after reducing the dimension of the data via either principal components or Fisher's discriminant analysis. We also explore the directional differences in observed images and present two parametric distributions, the generalized Laplacian and the Bessel K form, that well model the nonGaussian behavior of the directional differences. We then propose a model that labels each spatial site, using Bayesian inference and Markov random fields, that incorporates the information of the nonparametric distribution of the data, and the parametric distributions of the directional differences, along with a prior distribution that favors smooth labeling. We then test our model on actual hyperspectral data and present the results of our model, using the Washington D.C. Mall and Indian Springs rural area data sets.
Show less  Date Issued
 2004
 Identifier
 FSU_migr_etd2691
 Format
 Thesis
 Title
 Stochastic Models and Inferences for Commodity Futures Pricing.
 Creator

Ncube, Moeti M., Srivastava, Anuj, Doran, James, Mason, Patrick, Niu, Xufeng, Huﬀer, Fred, Wu, Wei, Department of Statistics, Florida State University
 Abstract/Description

The stochastic modeling of financial assets is essential to the valuation of financial products and investment decisions. These models are governed by certain parameters that are estimated through a process known as calibration. Current procedures typically perform a gridsearch optimization of a given objective function over a specified parameter space. These methods can be computationally intensive and require restrictions on the parameter space to achieve timely convergence. In this thesis...
Show moreThe stochastic modeling of financial assets is essential to the valuation of financial products and investment decisions. These models are governed by certain parameters that are estimated through a process known as calibration. Current procedures typically perform a gridsearch optimization of a given objective function over a specified parameter space. These methods can be computationally intensive and require restrictions on the parameter space to achieve timely convergence. In this thesis, we propose an alternative Kalman Smoother Expectation Maximization procedure (KSEM) that can jointly estimate all the parameters and produces better model t that compared to alternative estimation procedures. Further, we consider the additional complexity of the modeling of jumps or spikes that may occur in a time series. For this calibration we develop a Particle Smoother Expectation Maximization procedure (PSEM) for the optimization of nonlinear systems. This is an entirely new estimation approach, and we provide several examples of it's application.
Show less  Date Issued
 2009
 Identifier
 FSU_migr_etd2707
 Format
 Thesis
 Title
 A Bayesian Approach to MetaRegression: The Relationship Between Body Mass Index and AllCause Mortality.
 Creator

Marker, Mahtab, McGee, Dan, Hurt, Myra, Niu, Xiufeng, Huﬀer, Fred, Department of Statistics, Florida State University
 Abstract/Description

This thesis presents a Bayesian approach to MetaRegression and Individual Patient Data (IPD) Metaanalysis. The focus of the research is on establishing the relationship between Body Mass Index (BMI) and allcause mortality. This has been an area of continuing interest in the medical and public health communities and no concensus has been reached on what the optimal weight for individuals is. Standards are usually speci ed in terms of body mass index (BMI = wt(kg) over height(m)2 ) which is...
Show moreThis thesis presents a Bayesian approach to MetaRegression and Individual Patient Data (IPD) Metaanalysis. The focus of the research is on establishing the relationship between Body Mass Index (BMI) and allcause mortality. This has been an area of continuing interest in the medical and public health communities and no concensus has been reached on what the optimal weight for individuals is. Standards are usually speci ed in terms of body mass index (BMI = wt(kg) over height(m)2 ) which is associated with body fat percentage. Many studies in the literature have modelled the relationship between BMI and mortality and reported a variety of relationships including Ushaped, Jshaped and linear curves. The aim of my research was to use statistical methods to determine whether we can combine these diverse results an obtain single estimated relationship, using which one can nd the point of minimum mortality and establish reasonable ranges for optimal BMI or how we can best examine the reasons for the heterogeneity of results. Commonly used techniques of Metaanalysis and Metaregression are explored and a problem with the estimation procedure in the multivariate setting is presented. A Bayesian approach using Hierarchical Generalized Linear Mixed Model is suggested and implemented to overcome this drawback of standard estimation techniques. Another area which is explored briefly is that of Individual Patient Data metaanalysis. A Frailty model or Random Effects Proportional Hazards Survival model approach is proposed to carry out IPD metaregression and come up with a single estimated relationship between BMI and mortality, adjusting for the variation between studies.
Show less  Date Issued
 2007
 Identifier
 FSU_migr_etd2736
 Format
 Thesis
 Title
 Statistical Modelling and Applications of Neural Spike Trains.
 Creator

Lawhern, Vernon, Wu, Wei, Contreras, Robert J., Srivastava, Anuj, Huﬀer, Fred, Niu, Xufeng, Department of Statistics, Florida State University
 Abstract/Description

In this thesis we investigate statistical modelling of neural activity in the brain. We first develop a framework which is an extension of the statespace Generalized Linear Model (GLM) by Eden and colleagues [20] to include the effects of hidden states. These states, collectively, represent variables which are not observed (or even observable) in the modeling process but nonetheless can have an impact on the neural activity. We then develop a framework that allows us to input apriori target...
Show moreIn this thesis we investigate statistical modelling of neural activity in the brain. We first develop a framework which is an extension of the statespace Generalized Linear Model (GLM) by Eden and colleagues [20] to include the effects of hidden states. These states, collectively, represent variables which are not observed (or even observable) in the modeling process but nonetheless can have an impact on the neural activity. We then develop a framework that allows us to input apriori target information into the model. We examine both of these modelling frameworks on motor cortex data recorded from monkeys performing different targetdriven hand and arm movement tasks. Finally, we perform temporal coding analysis of sensory stimulation using principled statistical models and show the efficacy of our approach.
Show less  Date Issued
 2011
 Identifier
 FSU_migr_etd3251
 Format
 Thesis
 Title
 Statistical Models on Human Shapes with Application to Bayesian Image Segmentation and Gait Recognition.
 Creator

Kaziska, David M., Srivastava, Anuj, Mio, Washington, Chicken, Eric, Wegkamp, Marten, Department of Statistics, Florida State University
 Abstract/Description

In this dissertation we develop probability models for human shapes and apply those probability models to the problems of image segmentation and human identi_cation by gait recognition. To build probability models on human shapes, we consider human shape to be realizations of random variables on a space of simple closed curves and a space of elastic curves. Both of these spaces are quotient spaces of in_nite dimensional manifolds. Our probability models arise through Tangent Principal...
Show moreIn this dissertation we develop probability models for human shapes and apply those probability models to the problems of image segmentation and human identi_cation by gait recognition. To build probability models on human shapes, we consider human shape to be realizations of random variables on a space of simple closed curves and a space of elastic curves. Both of these spaces are quotient spaces of in_nite dimensional manifolds. Our probability models arise through Tangent Principal Component Analysis, a method of studying probability models on manifolds by projecting them onto a tangent plane to the manifold. Since we put the tangent plane at the Karcher mean of sample shapes, we begin our study by examining statistical properties of Karcher means on manifolds. We derive theoretical results for the location of Karcher means on certain manifolds, and perform a simulation study of properties of Karcher means on our shape space. Turning to the speci_c problem of distributions on human shapes we examine alternatives for probability models and _nd that kernel density estimators perform well. We use this model to sample shapes and to perform shape testing. The _rst application we consider is human detection in infrared images. We pursue this application using Bayesian image segmentation, in which our proposed human in an image is a maximum likelihood estimate, obtained using a prior distribution on human shapes and a likelihood arising from a divergence measure on the pixels in the image. We then consider human identi_cation by gait recognition. We examine human gait as a cyclostationary process on the space of elastic curves and develop a metric on processes based on the geodesic distance between sequences on that space. We develop and demonstrate a framework for gait recognition based on this metric, which includes the following elements: automatic detection of gait cycles, interpolation to register gait cycles, computation of a mean gait cycle, and identi_cation by matching a test cycle to the nearest member of a training set. We perform the matching both by an exhaustive search of the training set and through an expedited method using clusterbased trees and boosting.
Show less  Date Issued
 2005
 Identifier
 FSU_migr_etd3275
 Format
 Thesis
 Title
 A Statistical Approach to an Ocean Circulation Inverse Problem.
 Creator

Choi, Seoeun, Huﬀer, Fred W., Speer, Kevin G., Nolder, Craig, Niu, Xufeng, Wu, Wei, Department of Statistics, Florida State University
 Abstract/Description

This dissertation presents, applies, and evaluates a statistical approach to an ocean circulation problem. The objective is to produce a map of ocean velocity in the North Atlantic based on sparse measurements along ship tracks, based on a Bayesian approach with a physical model. The Stommel Gulf Stream model which relates the wind stress curl to the transport stream function is the physical model. A Gibbs sampler is used to extract features from the posterior velocity field. To specify the...
Show moreThis dissertation presents, applies, and evaluates a statistical approach to an ocean circulation problem. The objective is to produce a map of ocean velocity in the North Atlantic based on sparse measurements along ship tracks, based on a Bayesian approach with a physical model. The Stommel Gulf Stream model which relates the wind stress curl to the transport stream function is the physical model. A Gibbs sampler is used to extract features from the posterior velocity field. To specify the prior, the equation of the Stommel Gulf Stream model on a twodimensional grid is used.Comparisons with earlier approaches used by oceanographers are also presented.
Show less  Date Issued
 2007
 Identifier
 FSU_migr_etd3758
 Format
 Thesis
 Title
 Revealing Sparse Signals in Functional Data.
 Creator

Ivanescu, Andrada E. (Andrada Eugenia), Bunea, Florentina, Wegkamp, Marten, Gert, Joshua, Niu, Xufeng, Hollander, Myles, Department of Statistics, Florida State University
 Abstract/Description

My dissertation presents a novel statistical method to estimate a sparse signal in functional data and to construct confidence bands for the signal. Existing methods for inference for the mean function in this framework include smoothing splines and kernel estimates. Our methodology involves thresholding a least squares estimator, and the threshold level depends on the sources of variability that exist in this type of data. The proposed estimation method and the confidence bands successfully...
Show moreMy dissertation presents a novel statistical method to estimate a sparse signal in functional data and to construct confidence bands for the signal. Existing methods for inference for the mean function in this framework include smoothing splines and kernel estimates. Our methodology involves thresholding a least squares estimator, and the threshold level depends on the sources of variability that exist in this type of data. The proposed estimation method and the confidence bands successfully adapt to the sparsity of the signal. We present supporting evidence through simulations and applications to real datasets.
Show less  Date Issued
 2008
 Identifier
 FSU_migr_etd3852
 Format
 Thesis
 Title
 Time Scales in Epidemiological Analysis.
 Creator

Chalise, Prabhakar, McGee, Daniel L., Chicken, Eric, Carlson, Elwood, Sinha, Debajyoti, Department of Statistics, Florida State University
 Abstract/Description

The Cox proportional hazards model is routinely used to determine the time until an event of interest. Two time scales are used in practice: follow up time and chronological age. The former is the most frequently used time scale both in clinical studies and longitudinal observational studies. However, there is no general consensus about which time scale is the best. In recent years, papers have appeared arguing for using chronological age as the time scale either with or without adjusting the...
Show moreThe Cox proportional hazards model is routinely used to determine the time until an event of interest. Two time scales are used in practice: follow up time and chronological age. The former is the most frequently used time scale both in clinical studies and longitudinal observational studies. However, there is no general consensus about which time scale is the best. In recent years, papers have appeared arguing for using chronological age as the time scale either with or without adjusting the entryage. Also, it has been asserted that if the cumulative baseline hazard is exponential or if the ageatentry is independent of covariate, the two models are equivalent. Our studies do not satisfy these two conditions in general. We found that the true factor that makes the models perform significantly different is the variability in the ageatentry. If there is no variability in the entryage, time scales do not matter and both models estimate exactly the same coefficients. As the variability increases the models disagree with each other. We also computed the optimum time scale proposed by Oakes and utilized them for the Cox model. Both of our empirical and simulation studies show that follow up time scale model using age at entry as a covariate is better than the chronological age and Oakes time scale models. This finding is illustrated with two examples with data from Diverse Population Collaboration. Based on our findings, we recommend using follow up time as a time scale for epidemiological analysis.
Show less  Date Issued
 2009
 Identifier
 FSU_migr_etd3933
 Format
 Thesis
 Title
 Modeling Differential Item Functioning (DIF) Using Multilevel Logistic Regression Models: A Bayesian Perspective.
 Creator

Chaimongkol, Saengla, Huﬀer, Fred W., Kamata, Akihito, Tate, Richard, Niu, XuFeng, McGee, Daniel, Department of Statistics, Florida State University
 Abstract/Description

A multilevel logistic regression approach provides an attractive and practical alternative for the study of Differential Item Functioning (DIF). It is not only useful for identifying items with DIF but also for explaining the presence of DIF. Kamata and Binici (2003) first attempted to identify group unit characteristic variables explaining the variation of DIF by using hierarchical generalized linear models. Their models were implemented by the HLM5 software, which uses the penalized or...
Show moreA multilevel logistic regression approach provides an attractive and practical alternative for the study of Differential Item Functioning (DIF). It is not only useful for identifying items with DIF but also for explaining the presence of DIF. Kamata and Binici (2003) first attempted to identify group unit characteristic variables explaining the variation of DIF by using hierarchical generalized linear models. Their models were implemented by the HLM5 software, which uses the penalized or predictive quasilikelihood (PQL) method. They found that the variance estimates produced by HLM5 for the level 3 parameters are substantially negatively biased. This study extends their work by using a Bayesian approach to obtain more accurate parameter estimates. Two different approaches to modeling the DIF will be presented. These are referred to as the relative and mixture distribution approach, respectively. The relative approach measures the DIF of a particular item relative to the mean overall DIF for all items in the test. The mixture distribution approach treats the DIF as independent values drawn from a distribution which is a mixture of a normal distribution and a discrete distribution concentrated at zero. A simulation study is presented to assess the adequacy of the proposed models. This work also describes and studies models which allow the DIF to vary at level 3 (from school to school). In an example using real data, it is shown how the models can be applied to the identification of items with DIF and the explanation of the source of the DIF.
Show less  Date Issued
 2005
 Identifier
 FSU_migr_etd3939
 Format
 Thesis
 Title
 New Semiparametric Methods for Recurrent Events Data.
 Creator

Gu, Yu, Sinha, Debajyoti, Eberstein, Isaac W., McGee, Dan, Niu, Xufeng, Department of Statistics, Florida State University
 Abstract/Description

Recurrent events data are rising in all areas of biomedical research. We present a model for recurrent events data with the same link for the intensity and mean functions. Simple interpretations of the covariate effects on both the intensity and mean functions lead to a better understanding of the covariate effects on the recurrent events process. We use partial likelihood and empirical Bayes methods for inference and provide theoretical justifications and as well as relationships between...
Show moreRecurrent events data are rising in all areas of biomedical research. We present a model for recurrent events data with the same link for the intensity and mean functions. Simple interpretations of the covariate effects on both the intensity and mean functions lead to a better understanding of the covariate effects on the recurrent events process. We use partial likelihood and empirical Bayes methods for inference and provide theoretical justifications and as well as relationships between these methods. We also show the asymptotic properties of the empirical Bayes estimators. We illustrate the computational convenience and implementation of our methods with the analysis of a heart transplant study. We also propose an additive regression model and associated empirical Bayes method for the risk of a new event given the history of the recurrent events. Both the cumulative mean and rate functions have closed form expressions for our model. Our inference method for the simiparametric model is based on maximizing a finite dimensional integrated likelihood obtained by integrating over the nonparametric cumulative baseline hazard function. Our method can accommodate timevarying covariates and is easier to implement computationally instead of iterative algorithm based full Bayes methods. The asymptotic properties of our estimates give the largesample justifications from a frequentist stand point. We apply our method on a study of heart transplant patients to illustrate the computational convenience and other advantages of our method.
Show less  Date Issued
 2011
 Identifier
 FSU_migr_etd3941
 Format
 Thesis
 Title
 Quasi3D Statistical Inversion of Oceanographic Tracer Data.
 Creator

Herbei, Radu, Speer, Kevin, Wegkamp, Marten, Laurent, Louis St., Huﬀer, Fred, Niu, Xufeng, Department of Statistics, Florida State University
 Abstract/Description

We perform a quasi3D Bayesian inversion of oceanographic tracer data from the South Atlantic Ocean. Initially we are considering one active neutral density layer with an upper and lower boundary. The available hydrographic data is linked to model parameters (water velocities, diffusion coefficients) via a 3D advectiondiffusion equation. A robust solution to the inverse problem considered can be attained by introducing prior information about parameters and modeling the observation error....
Show moreWe perform a quasi3D Bayesian inversion of oceanographic tracer data from the South Atlantic Ocean. Initially we are considering one active neutral density layer with an upper and lower boundary. The available hydrographic data is linked to model parameters (water velocities, diffusion coefficients) via a 3D advectiondiffusion equation. A robust solution to the inverse problem considered can be attained by introducing prior information about parameters and modeling the observation error. This approach estimates both horizontal and vertical flow as well as diffusion coefficients. We find a system of alternating zonal jets at the depths of the North Atlantic Deep Water, consistent with direct measurements of flow and concentration maps. A uniqueness analysis of our model is performed in terms of the oxygen consumption rate. The vertical mixing coefficient bears some relation to the bottom topography even though we do not incorporate that into our model. We extend the method to a multilayer model, using thermal wind relations weakly in a local fashion (as opposed to integrating the entire water column) to connect layers vertically. Results suggest that the estimated deep zonal jets extend vertically, with a clear depth dependent structure. The vertical structure of the flow field is modified by the tracer fields over that set a priori by thermal wind. Our estimates are consistent with observed flow at the depths of the Antarctic Intermediate Water; at still shallower depths, above the layers considered here, the subtropical gyre is a significant feature of the horizontal flow.
Show less  Date Issued
 2006
 Identifier
 FSU_migr_etd4101
 Format
 Thesis
 Title
 Bayesian Dynamic Survival Models for Longitudinal Aging Data.
 Creator

He, Jianghua, McGee, Daniel L., Niu, Xufeng, Johnson, Suzanne B., Huﬀer, Fred W., Department of Statistics, Florida State University
 Abstract/Description

In this study, we will examine the Bayesian Dynamic Survival Models, timevarying coefficients models from a Bayesian perspective, and their applications in the aging setting. The specific questions we are interested in are: Do the relative importance of characteristics measured at a particular age, such as blood pressure, smoking, and body weight, with respect to heart diseases or death change as people age? If they do, how can we model the change? And, how does the change affect the...
Show moreIn this study, we will examine the Bayesian Dynamic Survival Models, timevarying coefficients models from a Bayesian perspective, and their applications in the aging setting. The specific questions we are interested in are: Do the relative importance of characteristics measured at a particular age, such as blood pressure, smoking, and body weight, with respect to heart diseases or death change as people age? If they do, how can we model the change? And, how does the change affect the analysis results if fixedeffect models are applied? In the epidemiological and statistical literature, the relationship between a risk factor and the risk of an event is often described in terms of the numerical contribution of the risk factor to the total risk within a followup period, using methods such as contingency tables and logistic regression models. With the development of survival analysis, another method named the Proportional Hazards Model becomes more popular. This model describes the relationship between a covariate and risk within a followup period as a process, under the assumption that the hazard ratio of the covariate is fixed during the followup period. Neither previous methods nor the Proportional Hazards Model allows the effect of a covariates to change flexibly with time. In these study, we intend to investigate some classic epidemiological relationships using appropriate methods that allow coefficients to change with time, and compare our results with those found in the literature. After describing what has been done in previous work based on multiple logistic regression or discriminant function analysis, we summarize different methods for estimating the time varying coefficient survival models that are developed specifically for the situations under which the proportional hazards assumption is violated. We will focus on the Bayesian Dynamic Survival Model because its flexibility and Bayesian structure fits our study goals. There are two estimation methods for the Bayesian Dynamic Survival Models, the Linear Bayesian Estimation (LBE) method and the Markov Chain Monte Carlo (MCMC) sampling method. The LBE method is simpler, faster, and more flexible to calculate, but it requires specifications of some parameters that usually are unknown. The MCMC method gets around the difficulty of specifying parameters, but is much more computationally intensive. We will use a simulation study to investigate the performances of these two methods, and provide suggestions on how to use them effectively in application. The Bayesian Dynamic Survival Model is applied to the Framingham Heart Study to investigate the timevarying effects of covariates such as gender, age, smoking, and SBP (Systolic Blood Pressure) with respect to death. We also examined the changing relationship between BMI (Body Mass Index) and allcause mortality, and suggested that some of the heterogeneity observed in the results found in the literature is likely to be a consequence of using fixed effect models to describe a timevarying relationship.
Show less  Date Issued
 2007
 Identifier
 FSU_migr_etd4174
 Format
 Thesis
 Title
 Investigating the Categories for Cholesterol and Blood Pressure for Risk Assessment of Death Due to Coronary Heart Disease.
 Creator

Franks, Billy J., McGee, Daniel, Hurt, Myra, Huﬀer, Fred, Niu, Xufeng, Department of Statistics, Florida State University
 Abstract/Description

Many characteristics for predicting death due to coronary heart disease are measured on a continuous scale. These characteristics, however, are often categorized for clinical use and to aid in treatment decisions. We would like to derive a systematic approach to determine the best categorizations of systolic blood pressure and cholesterol level for use in identifying individuals who are at high risk for death due to coronary heart disease and to compare these data derived categories to those...
Show moreMany characteristics for predicting death due to coronary heart disease are measured on a continuous scale. These characteristics, however, are often categorized for clinical use and to aid in treatment decisions. We would like to derive a systematic approach to determine the best categorizations of systolic blood pressure and cholesterol level for use in identifying individuals who are at high risk for death due to coronary heart disease and to compare these data derived categories to those in common usage. Whatever categories are chosen, they should allow physicians to accurately estimate the probability of survival from coronary heart disease until some time t. The best categories will be those that provide the most accurate prediction for an individual's risk of dying by t. The approach that will be used to determine these categories will be a version of Classification And Regression Trees that can be applied to censored survival data. The major goals of this dissertation are to obtain dataderived categories for risk assessment, compare these categories to the ones already recommended in the medical community, and to assess the performance of these categories in predicting survival probabilities.
Show less  Date Issued
 2005
 Identifier
 FSU_migr_etd4402
 Format
 Thesis
 Title
 Estimation and Sequential Monitoring of Nonlinear Functional Responses Using Wavelet Shrinkage.
 Creator

Cuevas, Jordan, Chicken, Eric, Sobanjo, John, Niu, Xufeng, Wu, Wei, Department of Statistics, Florida State University
 Abstract/Description

Statistical process control (SPC) is widely used in industrial settings to monitor processes for shifts in their distributions. SPC is generally thought of in two distinct phases: Phase I, in which historical data is analyzed in order to establish an incontrol process, and Phase II, in which new data is monitored for deviations from the incontrol form. Traditionally, SPC had been used to monitor univariate (multivariate) processes for changes in a particular parameter (parameter vector)....
Show moreStatistical process control (SPC) is widely used in industrial settings to monitor processes for shifts in their distributions. SPC is generally thought of in two distinct phases: Phase I, in which historical data is analyzed in order to establish an incontrol process, and Phase II, in which new data is monitored for deviations from the incontrol form. Traditionally, SPC had been used to monitor univariate (multivariate) processes for changes in a particular parameter (parameter vector). Recently however, technological advances have resulted in processes in which each observation is actually an ndimensional functional response (referred to as a profile), where n can be quite large. Additionally, these profiles are often unable to be adequately represented parametrically, making traditional SPC techniques inapplicable. This dissertation starts out by addressing the problem of nonparametric function estimation, which would be used to analyze process data in a PhaseI setting. The translation invariant wavelet estimator (TI) is often used to estimate irregular functions, despite the drawback that it tends to oversmooth jumps. A trimmed translation invariant estimator (TTI) is proposed, of which the TI estimator is a special case. By reducing the point by point variability of the TI estimator, TTI is shown to retain the desirable qualities of TI while improving reconstructions of functions with jumps. Attention is then turned to the PhaseII problem of monitoring sequences of profiles for deviations from incontrol. Two profile monitoring schemes are proposed; the first monitors for changes in the noise variance using a likelihood ratio test based on the highest detail level of wavelet coefficients of the observed profile. The second offers a semiparametric test to monitor for changes in both the functional form and noise variance. Both methods make use of wavelet shrinkage in order to distinguish relevant functional information from noise contamination. Different forms of each of these test statistics are proposed and results are compared via Monte Carlo simulation.
Show less  Date Issued
 2012
 Identifier
 FSU_migr_etd4788
 Format
 Thesis
 Title
 Weighted Adaptive Methods for Multivariate Response Models with an HIV/Neurocognitive Application.
 Creator

Geis, Jennifer Ann, She, Yiyuan, MeyerBaese, Anke, Barbu, Adrian, Bunea, Florentina, Niu, Xufeng, Department of Statistics, Florida State University
 Abstract/Description

Multivariate response models are being used increasingly more in almost all fields with the necessary employment of inferential methods such as Canonical Correlation Analysis (CCA). This requires the estimation of the number of uncorrelated canonical relationships between the two sets, or, equivalently so, determining the rank of the coefficient estimator in the multivariate response model.One way to do this is by the Rank Selection Criterion (RSC) by Bunea et al. with the assumption the...
Show moreMultivariate response models are being used increasingly more in almost all fields with the necessary employment of inferential methods such as Canonical Correlation Analysis (CCA). This requires the estimation of the number of uncorrelated canonical relationships between the two sets, or, equivalently so, determining the rank of the coefficient estimator in the multivariate response model.One way to do this is by the Rank Selection Criterion (RSC) by Bunea et al. with the assumption the error matrix has independent constant variance entries. While this assumption is necessary to show their strong theoretical results, in practical application, some flexibility is required. That is, such assumption cannot always be safely made. What is developed here are the theoretics that parallel Bunea et al.'s work with the addition of a "decorrelator" weight matrix. One choice for the weight matrix is the residual covariance, but this introduces many issues in practice. A computationally more convenient weight matrix is the sample response covariance. When such a weight matrix is chosen, CCA is directly accessible by this weighted version of RSC giving rise to an Adaptive CCA (ACCA) with principal proofs for the large sample setting. However, particular considerations are required for the highdimensional setting, where similar theoretics do not hold. What is offered instead are extensive empirical simulations that reveal that using the sample response covariance still provides good rank recovery and estimation of the coefficient matrix, and hence, also provides good estimation of the number of canonical relationships and variates. It is argued precisely why other versions of the residual covariance, including a regularized version, are poor choices in the highdimensional setting. Another approach to avoid these issues is to employ some type of variable selection methodology first before applying ACCA. Truly, any group selection method may be applied prior to ACCA as variable selection in the multivariate response model is the same as group selection in the univariate response model and thus completely eliminates these highdimensional concerns. To offer a practical application of these ideas, ACCA is applied to a "large sample'" neurocognitive dataset. Then, a highdimensional dataset is generated to which Group LASSO will be first utilized before ACCA. This provides a unique perspective into the relationships between cognitive deficiencies in HIVpositive patients and the extensive, available neuroimaging measures.
Show less  Date Issued
 2012
 Identifier
 FSU_migr_etd4861
 Format
 Thesis
 Title
 Prediction and Testing for NonParametric Random Function Signals in a Complex System.
 Creator

Hill, Paul C., Chicken, Eric, Klassen, Eric, Niu, Xufeng, Barbu, Adrian, Department of Statistics, Florida State University
 Abstract/Description

Methods employed in the construction of prediction bands for continuous curves require a dierent approach to those used for a data point. In many cases, the underlying function is unknown and thus a distributionfree approach which preserves sufficient coverage for the entire signal is necessary in the signal analysis. This paper discusses three methods for the formation of (1alpha)100% bootstrap prediction bands and their performances are compared through the coverage probabilities obtained...
Show moreMethods employed in the construction of prediction bands for continuous curves require a dierent approach to those used for a data point. In many cases, the underlying function is unknown and thus a distributionfree approach which preserves sufficient coverage for the entire signal is necessary in the signal analysis. This paper discusses three methods for the formation of (1alpha)100% bootstrap prediction bands and their performances are compared through the coverage probabilities obtained for each technique. Bootstrap samples are first obtained for the signal and then three dierent criteria are provided for the removal of 100% of the curves resulting in the (1alpha)100% prediction band. The first method uses the L1 distance between the upper and lower curves as a gauge to extract the widest bands in the dataset of signals. Also investigated are extractions using the Hausdorffdistance between the bounds as well as an adaption to the bootstrap intervals discussed in Lenhoffet al (1999). The bootstrap prediction bands each have good coverage probabilities for the continuous signals in the dataset. For a 95% prediction band, the coverage obtained were 90.59%, 93.72% and 95% for the L1 Distance, Hausdorff Distance and the adjusted Bootstrap methods respectively. The methods discussed in this paper have been applied to constructing prediction bands for spring discharge in a successful manner giving good coverage in each case. Spring Discharge measured over time can be considered as a continuous signal and the ability to predict the future signals of spring discharge is useful for monitoring flow and other issues related to the spring. While in some cases, rainfall has been tted with the gamma distribution, the discharge of the spring represented as continuous curves, is better approached not assuming any specific distribution. The Bootstrap aspect occurs not in sampling the output discharge curves but rather in simulating the input recharge that enters the spring. Bootstrapping the rainfall as described in this paper, allows for adequately creating new samples over different periods of time as well as specic rain events such as hurricanes or drought. The Bootstrap prediction methods put forth in this paper provide an approach that supplies adequate coverage for prediction bands for signals represented as continuous curves. The pathway outlined by the flow of the discharge through the springshed is described as a tree. A nonparametric pairwise test, motivated by the idea of Kmeans clustering, is proposed to decipher whether there is equality between two trees in terms of their discharges. A large sample approximation is devised for this lowertail significance test and test statistics for different numbers of input signals are compared to a generated table of critical values.
Show less  Date Issued
 2012
 Identifier
 FSU_migr_etd4910
 Format
 Thesis
 Title
 Riemannian Shape Analysis of Curves and Surfaces.
 Creator

Kurtek, Sebastian, Srivastava, Anuj, Klassen, Eric, Wu, Wei, Huﬀer, Fred, Dryden, Ian, Department of Statistics, Florida State University
 Abstract/Description

Shape analysis of curves and surfaces is a very important tool in many applications ranging from computer vision to bioinformatics and medical imaging. There are many difficulties when analyzing shapes of parameterized curves and surfaces. Firstly, it is important to develop representations and metrics such that the analysis is invariant to parameterization in addition to the standard transformations (rigid motion and scaling). Furthermore, under the chosen representations and metrics, the...
Show moreShape analysis of curves and surfaces is a very important tool in many applications ranging from computer vision to bioinformatics and medical imaging. There are many difficulties when analyzing shapes of parameterized curves and surfaces. Firstly, it is important to develop representations and metrics such that the analysis is invariant to parameterization in addition to the standard transformations (rigid motion and scaling). Furthermore, under the chosen representations and metrics, the analysis must be performed on infinitedimensional and sometimes nonlinear spaces, which poses an additional difficulty. In this work, we develop and apply methods which address these issues. We begin by defining a framework for shape analysis of parameterized open curves and extend these ideas to shape analysis of surfaces. We utilize the presented frameworks in various classification experiments spanning multiple application areas. In the case of curves, we consider the problem of clustering DTMRI brain fibers, classification of protein backbones, modeling and segmentation of signatures and statistical analysis of biosignals. In the case of surfaces, we perform disease classification using 3D anatomical structures in the brain, classification of handwritten digits by viewing images as quadrilateral surfaces, and finally classification of cropped facial surfaces. We provide two additional extensions of the general shape analysis frameworks that are the focus of this dissertation. The first one considers shape analysis of marked spherical surfaces where in addition to the surface information we are given a set of manually or automatically generated landmarks. This requires additional constraints on the definition of the reparameterization group and is applicable in many domains, especially medical imaging and graphics. Second, we consider reflection symmetry analysis of planar closed curves and spherical surfaces. Here, we also provide an example of disease detection based on brain asymmetry measures. We close with a brief summary and a discussion of open problems, which we plan on exploring in the future.
Show less  Date Issued
 2012
 Identifier
 FSU_migr_etd4963
 Format
 Thesis
 Title
 Semiparametric Survival Analysis Using Models with LogLinear Median.
 Creator

Lin, Jianchang, Sinha, Debajyoti, Zhou, Yi, Lipsitz, Stuart, McGee, Dan, Niu, XuFeng, She, Yiyuan, Department of Statistics, Florida State University
 Abstract/Description

First, we present two novel semiparametric survival models with loglinear median regression functions for right censored survival data. These models are useful alternatives to the popular Cox (1972) model and linear transformation models (Cheng et al., 1995). Compared to existing semiparametric models, our models have many important practical advantages, including interpretation of the regression parameters via the median and the ability to address heteroscedasticity. We demonstrate that our...
Show moreFirst, we present two novel semiparametric survival models with loglinear median regression functions for right censored survival data. These models are useful alternatives to the popular Cox (1972) model and linear transformation models (Cheng et al., 1995). Compared to existing semiparametric models, our models have many important practical advantages, including interpretation of the regression parameters via the median and the ability to address heteroscedasticity. We demonstrate that our modeling techniques facilitate the ease of prior elicitation and computation for both parametric and semiparametric Bayesian analysis of survival data. We illustrate the advantages of our modeling, as well as model diagnostics, via reanalysis of a smallcell lung cancer study. Results of our simulation study provide further guidance regarding appropriate modelling in practice. Our second goal is to develop the methods of analysis and associated theoretical properties for interval censored and current status survival data. These new regression models use loglinear regression function for the median. We present frequentist and Bayesian procedures for estimation of the regression parameters. Our model is a useful and practical alternative to the popular semiparametric models which focus on modeling the hazard function. We illustrate the advantages and properties of our proposed methods via reanalyzing a breast cancer study. Our other aim is to develop a model which is able to account for the heteroscedasticity of response, together with robust parameter estimation and outlier detection using sparsity penalization. Some preliminary simulation studies have been conducted to compare the performance of proposed model and existing median lasso regression model. Considering the estimation bias, mean squared error and other identication benchmark measures, our proposed model performs better than the competing frequentist estimator.
Show less  Date Issued
 2012
 Identifier
 FSU_migr_etd4992
 Format
 Thesis
 Title
 A Riemannian Framework for Annotated Curves Analysis.
 Creator

Liu, Wei, Srivastava, Anuj, Zhang, Jinfeng, Klassen, Eric P., Huﬀer, Fred, Department of Statistics, Florida State University
 Abstract/Description

We propose a Riemannian framework for shape analysis of annotated curves, curves that have certain attributes defined along them, in addition to their geometries.These attributes may be in form of vectorvalued functions, discrete landmarks, or symbolic labels, and provide auxiliary information along the curves. The resulting shape analysis, that is comparing, matching, and deforming, is naturally influenced by the auxiliary functions. Our idea is to construct curves in higher dimensions...
Show moreWe propose a Riemannian framework for shape analysis of annotated curves, curves that have certain attributes defined along them, in addition to their geometries.These attributes may be in form of vectorvalued functions, discrete landmarks, or symbolic labels, and provide auxiliary information along the curves. The resulting shape analysis, that is comparing, matching, and deforming, is naturally influenced by the auxiliary functions. Our idea is to construct curves in higher dimensions using both geometric and auxiliary coordinates, and analyze shapes of these curves. The difficulty comes from the need for removing different groups from different components: the shape is invariant to rigidmotion, global scale and reparameterization while the auxiliary component is usually invariant only to the reparameterization. Thus, the removal of some transformations (rigid motion and global scale) is restricted only to the geometric coordinates, while the reparameterization group is removed for all coordinates. We demonstrate this framework using a number of experiments.
Show less  Date Issued
 2011
 Identifier
 FSU_migr_etd4997
 Format
 Thesis
 Title
 A Novel Riemannian Metric for Analyzing Spherical Functions with Applications to HARDI Data.
 Creator

Ncube, Sentibaleng, Srivastava, Anuj, Klassen, Eric, Wu, Wei, Niu, Xufeng, Department of Statistics, Florida State University
 Abstract/Description

We propose a novel Riemannian framework for analyzing orientation distribution functions (ODFs), or their probability density functions (PDFs), in HARDI data sets for use in comparing, interpolating, averaging, and denoising PDFs. This is accomplished by separating shape and orientation features of PDFs, and then analyzing them separately under their own Riemannian metrics. We formulate the action of the rotation group on the space of PDFs, and define the shape space as the quotient space of...
Show moreWe propose a novel Riemannian framework for analyzing orientation distribution functions (ODFs), or their probability density functions (PDFs), in HARDI data sets for use in comparing, interpolating, averaging, and denoising PDFs. This is accomplished by separating shape and orientation features of PDFs, and then analyzing them separately under their own Riemannian metrics. We formulate the action of the rotation group on the space of PDFs, and define the shape space as the quotient space of PDFs modulo the rotations. In other words, any two PDFs are compared in: (1) shape by rotationally aligning one PDF to another, using the FisherRao distance on the aligned PDFs, and (2) orientation by comparing their rotation matrices. This idea improves upon the results from using the FisherRao metric in analyzing PDFs directly, a technique that is being used increasingly, and leads to geodesic interpolations that are biologically feasible. This framework leads to definitions and efficient computations for the Karcher mean that provide tools for improved interpolation and denoising. We demonstrate these ideas, using an experimental setup involving several PDFs.
Show less  Date Issued
 2011
 Identifier
 FSU_migr_etd5064
 Format
 Thesis
 Title
 Nonparametric Data Analysis on Manifolds with Applications in Medical Imaging.
 Creator

Osborne, Daniel Eugene, Patrangenaru, Victor, Liu, Xiuwen, Barbu, Adrian, Chicken, Eric, Department of Statistics, Florida State University
 Abstract/Description

Over the past twenty years, there has been a rapid development in Nonparametric Statistical Analysis on Manifolds applied to Medical Imaging problems. In this body of work, we focus on two different medical imaging problems. The first problem corresponds to analyzing the CT scan data. In this context, we perform nonparametric analysis on the 3D data retrieved from CT scans of healthy young adults, on the SizeandReflection Shape Space of kads in general position in 3D. This work is a part...
Show moreOver the past twenty years, there has been a rapid development in Nonparametric Statistical Analysis on Manifolds applied to Medical Imaging problems. In this body of work, we focus on two different medical imaging problems. The first problem corresponds to analyzing the CT scan data. In this context, we perform nonparametric analysis on the 3D data retrieved from CT scans of healthy young adults, on the SizeandReflection Shape Space of kads in general position in 3D. This work is a part of larger project on planning reconstructive surgery in severe skull injuries which includes preprocessing and postprocessing steps of CT images. The next problem corresponds to analyzing MR diffusion tensor imaging data. Here, we develop a twosample procedure for testing the equality of the generalized Frobenius means of two independent populations on the space of symmetric positive matrices. These new methods, naturally lead to an analysis based on Cholesky decompositions of covariance matrices which helps to decrease computational time and does not increase dimensionality. The resulting nonparametric matrix valued statistics are used for testing if there is a difference on average between corresponding signals in Diffusion Tensor Images (DTI) in young children with dyslexia when compared to their clinically normal peers. The results presented here correspond to data that was previously used in the literature using parametric methods which also showed a significant difference.
Show less  Date Issued
 2012
 Identifier
 FSU_migr_etd5085
 Format
 Thesis
 Title
 MixedEffects Models for Count Data with Applications to Educational Research.
 Creator

Shin, Jihyung, Niu, Xufeng, Hu, Shouping, Al Otaiba, Stephanie Dent, McGee, Daniel, Wu, Wei, Department of Statistics, Florida State University
 Abstract/Description

This research is motivated by an analysis of reading research data. We are interested in modeling the test outcome of ability to fluently recode letters into sounds of kindergarten children aged between 5 and 7. The data showed excessive zero scores (more than 30% of children) on the test. In this dissertation, we carefully examine the models dealing with excessive zeros, which are based on the mixture of distributions, a distribution with zeros and a standard probability distribution with...
Show moreThis research is motivated by an analysis of reading research data. We are interested in modeling the test outcome of ability to fluently recode letters into sounds of kindergarten children aged between 5 and 7. The data showed excessive zero scores (more than 30% of children) on the test. In this dissertation, we carefully examine the models dealing with excessive zeros, which are based on the mixture of distributions, a distribution with zeros and a standard probability distribution with non negative values. In such cases, a log normal variable or a Poisson random variable is often observed with probability from semicontinuous data or count data. The previously proposed models, mixedeffects and mixeddistribution models (MEMD) by Tooze(2002) et al. for semicontinuous data and zeroinflated Poisson (ZIP) regression models by Lambert(1992) for count data are reviewed. We apply zeroinflated Poisson models to repeated measures data of zeroinflated data by introducing a pair of possibly correlated random effects to the zeroinflated Poisson model to accommodate withinsubject correlation and between subject heterogeneity. The model describes the effect of predictor variables on the probability of nonzero responses (occurrence) and mean of nonzero responses (intensity) separately. The likelihood function is maximized using dual quasiNewton optimization of an approximated by adaptive Gaussian quadrature. The maximum likelihood estimates are obtained through standard statistical software package. Using different model parameters, the number of subject, and the number of measurements per subject, the simulation study is conducted and the results are presented. The dissertation ends with the application of the model to reading research data and future research. We examine the number of correct letter sound counted of children collected over 2008 2009 academic year. We find that age, gender and socioeconomic status are significantly related to the letter sound fluency of children in both parts of the model. The model provides better explanation of data structure and easier interpretations of parameter values, as they are the same as in standard logistic models and Poisson regression models. The model can be extended to accommodate serial correlation which can be observed in longitudinal data. Also, one may consider multilevel zeroinflated Poisson model. Although the multilevel model was proposed previously, parameter estimation by penalized quasi likelihood methods is questionable, and further examination is needed.
Show less  Date Issued
 2012
 Identifier
 FSU_migr_etd5181
 Format
 Thesis
 Title
 The Relationship Between Body Mass and Blood Pressure in Diverse Populations.
 Creator

Abayomi, Emilola J., McGee, Daniel, Lackland, Daniel, Hurt, Myra, Chicken, Eric, Niu, Xufeng, Department of Statistics, Florida State University
 Abstract/Description

High blood pressure is a major determinant of risk for Coronary Heart Disease (CHD) and stroke, leading causes of death in the industrialized world. A myriad of pharmacological treatments for elevated blood pressure, defined as a blood pressure greater than 140/90mmHg, are available and have at least partially resulted in large reductions in the incidence of CHD and stroke in the U.S. over the last 50 years. The factors that may increase blood pressure levels are not well understood, but body...
Show moreHigh blood pressure is a major determinant of risk for Coronary Heart Disease (CHD) and stroke, leading causes of death in the industrialized world. A myriad of pharmacological treatments for elevated blood pressure, defined as a blood pressure greater than 140/90mmHg, are available and have at least partially resulted in large reductions in the incidence of CHD and stroke in the U.S. over the last 50 years. The factors that may increase blood pressure levels are not well understood, but body mass is thought to be a major determinant of blood pressure level. Obesity is measured through various methods (skinfolds, waisttohip ratio, bioelectrical impedance analysis (BIA), etc.), but the most commonly used measure is body mass index,BMI= Weight(kg)/Height(m)2
Show less  Date Issued
 2012
 Identifier
 FSU_migr_etd5308
 Format
 Thesis
 Title
 Monte Carlo Likelihood Estimation for Conditional Autoregressive Models with Application to Sparse Spatiotemporal Data.
 Creator

Bain, Rommel, Huffer, Fred, Becker, Betsy, Niu, Xufeng, Srivastava, Anuj, Department of Statistics, Florida State University
 Abstract/Description

Spatiotemporal modeling is increasingly used in a diverse array of fields, such as ecology, epidemiology, health care research, transportation, economics, and other areas where data arise from a spatiotemporal process. Spatiotemporal models describe the relationship between observations collected from different spatiotemporal sites. The modeling of spatiotemporal interactions arising from spatiotemporal data is done by incorporating the spacetime dependence into the covariance structure. A...
Show moreSpatiotemporal modeling is increasingly used in a diverse array of fields, such as ecology, epidemiology, health care research, transportation, economics, and other areas where data arise from a spatiotemporal process. Spatiotemporal models describe the relationship between observations collected from different spatiotemporal sites. The modeling of spatiotemporal interactions arising from spatiotemporal data is done by incorporating the spacetime dependence into the covariance structure. A main goal of spatiotemporal modeling is the estimation and prediction of the underlying process that generates the observations under study and the parameters that govern the process. Furthermore, analysis of the spatiotemporal correlation of variables can be used for estimating values at sites where no measurements exist. In this work, we develop a framework for estimating quantities that are functions of complete spatiotemporal data when the spatiotemporal data is incomplete. We present two classes of conditional autoregressive (CAR) models (the homogeneous CAR (HCAR) model and the weighted CAR (WCAR) model) for the analysis of sparse spatiotemporal data (the log of monthly mean zooplankton biomass) collected on a spatiotemporal lattice by the California Cooperative Oceanic Fisheries Investigations (CalCOFI). These models allow for spatiotemporal dependencies between nearest neighbor sites on the spatiotemporal lattice. Typically, CAR model likelihood inference is quite complicated because of the intractability of the CAR model's normalizing constant. Sparse spatiotemporal data further complicates likelihood inference. We implement Monte Carlo likelihood (MCL) estimation methods for parameter estimation of our HCAR and WCAR models. Monte Carlo likelihood estimation provides an approximation for intractable likelihood functions. We demonstrate our framework by giving estimates for several different quantities that are functions of the complete CalCOFI time series data.
Show less  Date Issued
 2013
 Identifier
 FSU_migr_etd7283
 Format
 Thesis
 Title
 Nonparametric Nonstationary Density Estimation Including Upper Control Limit Methods for Detecting Change Points.
 Creator

Becvarik, Rachel A., Chicken, Eric, Liu, Guosheng, Sinha, Debajyoti, Wu, Wei, Department of Statistics, Florida State University
 Abstract/Description

Nonstationary nonparametric densities occur naturally including applications such as monitoring the amount of toxins in the air and in monitoring internet streaming data. Progress has been made in estimating these densities, but there is little current work on monitoring them for changes. A new statistic is proposed which effectively monitors these nonstationary nonparametric densities through the use of transformed wavelet coefficients of the quantiles. This method is completely...
Show moreNonstationary nonparametric densities occur naturally including applications such as monitoring the amount of toxins in the air and in monitoring internet streaming data. Progress has been made in estimating these densities, but there is little current work on monitoring them for changes. A new statistic is proposed which effectively monitors these nonstationary nonparametric densities through the use of transformed wavelet coefficients of the quantiles. This method is completely nonparametric, designed for no particular distributional assumptions; thus making it effective in a variety of conditions. Existing methods for monitoring sequential data typically focus on using a single value upper control limit (UCL) based on a specified in control average run length (ARL) to detect changes in these nonstationary statistics. However, such a UCL is not designed to take into consideration the false alarm rate, the power associated with the test or the underlying distribution of the ARL. Additionally, if the monitoring statistic is known to be monotonic over time (which is typical in methods using maxima in their statistics, for example) the flat UCL does not adjust to this property. We propose several methods for creating UCLs that provide improved power and simultaneously adjust the false alarm rate to userspecified values. Our methods are constructive in nature, making no use of assumed distribution properties of the underlying monitoring statistic. We evaluate the different proposed UCLs through simulations to illustrate the improvements over current UCLs. The proposed method is evaluated with respect to profile monitoring scenarios and the proposed density statistic. The method is applicable for monitoring any monotonically nondecreasing nonstationary statistics.
Show less  Date Issued
 2013
 Identifier
 FSU_migr_etd7292
 Format
 Thesis
 Title
 Theories on Group Variable Selection in Multivariate Regression Models.
 Creator

Ha, SeungYeon, She, Yiyuan, Okten, Giray, Huffer, Fred, Sinha, Debajyoti, Department of Statistics, Florida State University
 Abstract/Description

We study group variable selection on multivariate regression model. Group variable selection is equivalent to select the nonzero rows of coefficient matrix, since there are multiple response variables and thus if one predictor is irrelevant to estimation then the corresponding row must be zero. In high dimensional setup, shrinkage estimation methods are applicable and guarantee smaller MSE than OLS according to JamesStein phenomenon (1961). As one of shrinkage methods, we study penalized...
Show moreWe study group variable selection on multivariate regression model. Group variable selection is equivalent to select the nonzero rows of coefficient matrix, since there are multiple response variables and thus if one predictor is irrelevant to estimation then the corresponding row must be zero. In high dimensional setup, shrinkage estimation methods are applicable and guarantee smaller MSE than OLS according to JamesStein phenomenon (1961). As one of shrinkage methods, we study penalized least square estimation for a group variable selection. Among them, we study L0 regularization and L0 + L2 regularization with the purpose of obtaining accurate prediction and consistent feature selection, and use the corresponding computational procedure Hard TISP and HardRidge TISP (She, 2009) to solve the numerical difficulties. These regularization methods show better performance both on prediction and selection than Lasso (L1 regularization), which is one of popular penalized least square method. L0 acheives the same optimal rate of prediction loss and estimation loss as Lasso, but it requires no restriction on design matrix or sparsity for controlling the prediction error and a relaxed condition than Lasso for controlling the estimation error. Also, for selection consistency, it requires much relaxed incoherence condition, which is correlation between the relevant subset and irrelevant subset of predictors. Therefore L0 can work better than Lasso both on prediction and sparsity recovery, in practical cases such that correlation is high or sparsity is not low. We study another method, L0 + L2 regularization which uses the combined penalty of L0 and L2. For the corresponding procedure HardRidge TISP, two parameters work independently for selection and shrinkage (to enhance prediction) respectively, and therefore it gives better performance on some cases (such as low signal strength) than L0 regularization. For L0 regularization, λ works for selection but it is tuned in terms of prediction accuracy. L0 + L2 regularization gives the optimal rate of prediction and estimation errors without any restriction, when the coefficient of l2 penalty is appropriately assigned. Furthermore, it can achieve a better rate of estimation error with an ideal choice of blockwise weight to l2 penalty.
Show less  Date Issued
 2013
 Identifier
 FSU_migr_etd7404
 Format
 Thesis
 Title
 Nonparametric Wavelet Thresholding and Profile Monitoring for NonGaussian Errors.
 Creator

McGinnity, Kelly, Chicken, Eric, Hoeﬂich, Peter, Niu, Xufeng, Zhang, Jinfeng, Department of Statistics, Florida State University
 Abstract/Description

Recent advancements in data collection allow scientists and researchers to obtain massive amounts of information in short periods of time. Often this data is functional and quite complex. Wavelet transforms are popular, particularly in the engineering and manufacturing fields, for handling these type of complicated signals. A common application of wavelets is in statistical process control (SPC), in which one tries to determine as quickly as possible if and when a sequence of profiles has...
Show moreRecent advancements in data collection allow scientists and researchers to obtain massive amounts of information in short periods of time. Often this data is functional and quite complex. Wavelet transforms are popular, particularly in the engineering and manufacturing fields, for handling these type of complicated signals. A common application of wavelets is in statistical process control (SPC), in which one tries to determine as quickly as possible if and when a sequence of profiles has gone outofcontrol. However, few wavelet methods have been proposed that don't rely in some capacity on the assumption that the observational errors are normally distributed. This dissertation aims to fill this void by proposing a simple, nonparametric, distributionfree method of monitoring profiles and estimating changepoints. Using only the magnitudes and location maps of thresholded wavelet coefficients, our method uses the spatial adaptivity property of wavelets to accurately detect profile changes when the signal is obscured with a variety of nonGaussian errors. Wavelets are also widely used for the purpose of dimension reduction. Applying a thresholding rule to a set of wavelet coefficients results in a "denoised" version of the original function. Once again, existing thresholding procedures generally assume independent, identically distributed normal errors. Thus, the second main focus of this dissertation is a nonparametric method of thresholding that does not assume Gaussian errors, or even that the form of the error distribution is known. We improve upon an existing evenodd crossvalidation method by employing block thresholding and level dependence, and show that the proposed method works well on both skewed and heavytailed distributions. Such thresholding techniques are essential to the SPC procedure developed above.
Show less  Date Issued
 2013
 Identifier
 FSU_migr_etd7502
 Format
 Thesis
 Title
 An Ensemble Approach to Predicting Health Outcomes.
 Creator

Nilles, Ester Kim, McGee, Dan, Zhang, Jinfeng, Eberstein, Isaac, Sinha, Debajyoti, Department of Statistics, Florida State University
 Abstract/Description

Heart disease and premature birth continue to be the leading cause of mortality and neonatal mortality in large parts of the world. They are also estimated to have the highest medical expenditures in the United States. Early detection of heart disease incidence plays a critical role in preserving heart health, and identifying pregnancies at high risk of premature birth is highly valuable information for early interventions. The past few decades, identification of patients at high health risk...
Show moreHeart disease and premature birth continue to be the leading cause of mortality and neonatal mortality in large parts of the world. They are also estimated to have the highest medical expenditures in the United States. Early detection of heart disease incidence plays a critical role in preserving heart health, and identifying pregnancies at high risk of premature birth is highly valuable information for early interventions. The past few decades, identification of patients at high health risk have been based on logistic regression or Cox proportional hazards models. In more recent years, machine learning models have grown in popularity within the medical field for their superior predictive and classification performances over the classical statistical models. However, their performances in heart disease and premature birth predictions have been comparable and inconclusive, leaving the question of which model most accurately reflects the data difficult to resolve. Our aim is to incorporate information learned by different models into one final model that will generate superior predictive performances. We first compare the widely used machine learning models  the multilayer perceptron network, knearest neighbor and support vector machine  to the statistical models logistic regression and Cox proportional hazards. Then the individual models are combined into one in an ensemble approach, also referred to as ensemble modeling. The proposed approaches include SSEweighted, AUCweighted, logistic and flexible naive Bayes. The individual models are unique and capture different aspects of the data, but as expected, no individual one outperforms any other. The ensemble approach is an easily computed method that eliminates the need to select one model, integrates the strengths of different models, and generates optimal performances. Particularly in cases where the risk factors associated to an outcome are elusive, such as in premature birth, the ensemble models significantly improve their prediction.
Show less  Date Issued
 2013
 Identifier
 FSU_migr_etd7530
 Format
 Thesis
 Title
 Meta Analysis and Meta Regression of a Measure of Discrimination Used in Prognostic Modeling.
 Creator

Rivera, Gretchen L., McGee, Daniel, Hurt, Myra, Niu, Xufeng, Sinha, Debajyoti, Department of Statistics, Florida State University
 Abstract/Description

In this paper we are interested in predicting death with the underlying cause of coronary heart disease (CHD). There are two prognostic modeling methods used to predict CHD: the logistic model and the proportional hazard model. For this paper we consider the logistic model. The dataset used is the Diverse Populations Collaboration (DPC) dataset which includes 28 studies. The DPC dataset has epidemiological results from investigation conducted in different populations around the world. For our...
Show moreIn this paper we are interested in predicting death with the underlying cause of coronary heart disease (CHD). There are two prognostic modeling methods used to predict CHD: the logistic model and the proportional hazard model. For this paper we consider the logistic model. The dataset used is the Diverse Populations Collaboration (DPC) dataset which includes 28 studies. The DPC dataset has epidemiological results from investigation conducted in different populations around the world. For our analysis we include those individuals who are 17 years old or older. The predictors are: age, diabetes, total serum cholesterol (mg/dl), high density lipoprotein (mg/dl), systolic blood pressure (mmHg) and if the participant is a current cigarette smoker. There is a natural grouping within the studies such as gender, rural or urban area and race. Based on these strata we have 84 cohort groups. Our main interest is to evaluate how well the prognostic model discriminates. For this, we used the area under the Receiver Operating Characteristic (ROC) curve. The main idea of the ROC curve is that a set of subject is known to belong to one of two classes (signal or noise group). Then an assignment procedure assigns each object to a class on the basis of information observed. The assignment procedure is not perfect: sometimes an object is misclassified. We want to evaluate the quality of performance of this procedure, for this we used the Area under the ROC curve (AUROC). The AUROC varies from 0.5 (no apparent accuracy) to 1.0 (perfect accuracy). For each logistic model we found the AUROC and its standard error (SE). We used Metaanalysis to summarize the estimated AUROCs and to evaluate if there is heterogeneity in our estimates. To evaluate the existence of significant heterogeneity we used the Q statistic. Since heterogeneity was found in our study we compare seven different methods for estimating τ2 (between study variance). We conclude by examining whether differences in study characteristics explained the heterogeneity in the values of the AUROC.
Show less  Date Issued
 2013
 Identifier
 FSU_migr_etd7580
 Format
 Thesis