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 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
 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
 Fused Lasso and Tensor Covariance Learning with Robust Estimation.
 Creator

Kunz, Matthew Ross, She, Yiyuan, Stiegman, Albert E., Mai, Qing, Chicken, Eric, Florida State University, College of Arts and Sciences, Department of Statistics
 Abstract/Description

With the increase in computation and data storage, there has been a vast collection of information gained with scientific measurement devices. However, with this increase in data and variety of domain applications, statistical methodology must be tailored to specific problems. This dissertation is focused on analyzing chemical information with an underlying structure. Robust fused lasso leverages information about the neighboring regression coefficient structure to create blocks of...
Show moreWith the increase in computation and data storage, there has been a vast collection of information gained with scientific measurement devices. However, with this increase in data and variety of domain applications, statistical methodology must be tailored to specific problems. This dissertation is focused on analyzing chemical information with an underlying structure. Robust fused lasso leverages information about the neighboring regression coefficient structure to create blocks of coefficients. Robust modifications are made to the mean to account for gross outliers in the data. This method is applied to near infrared spectral measurements in prediction of an aqueous analyte concentration and is shown to improve prediction accuracy. Expansion on the robust estimation and structure analysis is performed by examining graph structures within a clustered tensor. The tensor is subjected to wavelet smoothing and robust sparse precision matrix estimation for a detailed look into the covariance structure. This methodology is applied to catalytic kinetics data where the graph structure estimates the elementary steps within the reaction mechanism.
Show less  Date Issued
 2018
 Identifier
 2018_Fall_Kunz_fsu_0071E_14844
 Format
 Thesis
 Title
 Intensity Estimation in Poisson Processes with Phase Variability.
 Creator

Gordon, Glenna, Wu, Wei, Whyte, James, Srivastava, Anuj, Chicken, Eric, Florida State University, College of Arts and Sciences, Department of Statistics
 Abstract/Description

Intensity estimation for Poisson processes is a classical problem and has been extensively studied over the past few decades. However, current methods of intensity estimation assume phase variability or compositional noise, i.e. a nonlinear shift along the time axis, is nonexistent in the data which is an unreasonable assumption for practical observations. The key challenge is that these observations are not "aligned'', and registration procedures are required for successful estimation. As a...
Show moreIntensity estimation for Poisson processes is a classical problem and has been extensively studied over the past few decades. However, current methods of intensity estimation assume phase variability or compositional noise, i.e. a nonlinear shift along the time axis, is nonexistent in the data which is an unreasonable assumption for practical observations. The key challenge is that these observations are not "aligned'', and registration procedures are required for successful estimation. As a result, these estimation methods can yield estimators that are inefficient or that underperform in simulations and applications. This dissertation summarizes two key projects which examine estimation of the intensity of a Poisson process in the presence of phase variability. The first project proposes an alignmentbased framework for intensity estimation. First, it is shown that the intensity function is areapreserved with respect to compositional noise. Such a property implies that the time warping is only encoded in the density, or normalized intensity, function. Then, the intensity function can be decomposed into the product of the estimated total intensity (a scalar value) and the estimated density function. The estimation of the density relies on a metric which measures the phase difference between two density functions. An asymptotic study shows that the proposed estimation algorithm provides a consistent estimator for the normalized intensity. The success of the proposed estimation algorithm is illustrated using two simulations and the new framework is applied in a real data set of neural spike trains, showing that the proposed estimation method yields improved classification accuracy over previous methods. The second project utilizes 2014 Florida data from the Healthcare Cost and Utilization Project's State Inpatient Database and State Emergency Department Database (provided to the U.S. Department of Health and Human Services, Agency for Healthcare Research and Quality by the Florida Agency for Health Care Administration) to examine heart failure emergency department arrival times. Current estimation methods for examining emergency department arrival data ignore the functional nature of the data and implement naive analysis methods. In this dissertation, the arrivals are treated as a Poisson process and the intensity of the process is estimated using existing density estimation and function registration methods. The results of these analyses show the importance of considering the functional nature of emergency department arrival data and the critical role that function registration plays in the intensity estimation of the arrival process.
Show less  Date Issued
 2016
 Identifier
 FSU_FA2016_Gordon_fsu_0071E_13511
 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
 Methods of Block Thresholding Across Multiple Resolution Levels in Adaptive Wavelet Estimation.
 Creator

Schleeter, Tiffany M., Chicken, Eric, Clark, Kathleen M., Pati, Debdeep, Sinha, Debajyoti, Florida State University, College of Arts and Sciences, Department of Statistics
 Abstract/Description

Blocking methods of thresholding have demonstrated many advantages over termbyterm methods in adaptive wavelet estimation. These blocking methods are resolutionlevel specific, meaning the coefficients are grouped together only within the same resolution level. Techniques have not yet been proposed for blocking across multiple resolution levels and do not take into consideration varying shapes of blocks for wavelet coefficients. Presently, several methods of block thresholding across...
Show moreBlocking methods of thresholding have demonstrated many advantages over termbyterm methods in adaptive wavelet estimation. These blocking methods are resolutionlevel specific, meaning the coefficients are grouped together only within the same resolution level. Techniques have not yet been proposed for blocking across multiple resolution levels and do not take into consideration varying shapes of blocks for wavelet coefficients. Presently, several methods of block thresholding across multiple resolution levels are described. Various simulation studies analyze the use of these methods among nonparametric functions, including comparisons to other blocking and nonblocking wavelet thresholding methods. The introduction of a this new technique questions when this method will be advantageous over resolutionlevel specific methods. Another simulation study demonstrates a method of statistically selecting when blocking across resolution levels is beneficial over traditional techniques. Additional analysis will conclude how effective the automated selection method is in both simulation and if put into practice.
Show less  Date Issued
 2015
 Identifier
 FSU_migr_etd9677
 Format
 Thesis
 Title
 NonParametric and SemiParametric Estimation and Inference with Applications to Finance and Bioinformatics.
 Creator

Tran, Hoang Trong, She, Yiyuan, Ökten, Giray, Chicken, Eric, Niu, Xufeng, Tao, Minjing, Florida State University, College of Arts and Sciences, Department of Statistics
 Abstract/Description

In this dissertation, we develop tools from nonparametric and semiparametric statistics to perform estimation and inference. In the first chapter, we propose a new method called NonParametric Outlier Identification and Smoothing (NOIS), which robustly smooths stock prices, automatically detects outliers and constructs pointwise confidence bands around the resulting curves. In real world examples of highfrequency data, NOIS successfully detects erroneous prices as outliers and uncovers...
Show moreIn this dissertation, we develop tools from nonparametric and semiparametric statistics to perform estimation and inference. In the first chapter, we propose a new method called NonParametric Outlier Identification and Smoothing (NOIS), which robustly smooths stock prices, automatically detects outliers and constructs pointwise confidence bands around the resulting curves. In real world examples of highfrequency data, NOIS successfully detects erroneous prices as outliers and uncovers borderline cases for further study. NOIS can also highlight notable features and reveal new insights in interday chart patterns. In the second chapter, we focus on a method for nonparametric inference called empirical likelihood (EL). Computation of EL in the case of a fixed parameter vector is a convex optimization problem easily solved by Lagrange multipliers. In the case of a composite empirical likelihood (CEL) test where certain components of the parameter vector are free to vary, the optimization problem becomes nonconvex and much more difficult. We propose a new algorithm for the CEL problem named the BILinear Algorithm for Composite EmPirical Likelihood (BICEP). We extend the BICEP framework by introducing a new method called Robust Empirical Likelihood (REL) that detects outliers and greatly improves the inference in comparison to the nonrobust EL. The REL method is combined with CEL by the TRILinear Algorithm for Composite EmPirical Likelihood (TRICEP). We demonstrate the efficacy of the proposed methods on simulated and real world datasets. We present a novel semiparametric method for variable selection with interesting biological applications in the final chapter. In bioinformatics datasets the experimental units often have structured relationships that are nonlinear and hierarchical. For example, in microbiome data the individual taxonomic units are connected to each other through a phylogenetic tree. Conventional techniques for selecting relevant taxa either do not account for the pairwise dependencies between taxa, or assume linear relationships. In this work we propose a new framework for variable selection called SemiParametric Affinity Based Selection (SPAS), which has the flexibility to utilize struc tured and nonparametric relationships between variables. In synthetic data experiments SPAS outperforms existing methods and on real world microbiome datasets it selects taxa according to their phylogenetic similarities.
Show less  Date Issued
 2018
 Identifier
 2018_Sp_Tran_fsu_0071E_14477
 Format
 Thesis
 Title
 Nonlinear Multivariate Tests for HighDimensional Data Using Wavelets with Applications in Genomics and Engineering.
 Creator

Girimurugan, Senthil Balaji, Chicken, Eric, Zhang, Jinfeng, Ahlquist, Jon, Tao, Minjing, Department of Statistics, Florida State University
 Abstract/Description

Gaussian processes are not uncommon in various fields of science such as engineering, genomics, quantitative finance and astronomy, to name a few. In fact, such processes are special cases in a broader class of data known as functional data. When the underlying mean response of a process is a function, the resulting data from these processes are functional responses and specialized statistical tools are required in their analysis. The methodology discussed in this work offers nonparametric...
Show moreGaussian processes are not uncommon in various fields of science such as engineering, genomics, quantitative finance and astronomy, to name a few. In fact, such processes are special cases in a broader class of data known as functional data. When the underlying mean response of a process is a function, the resulting data from these processes are functional responses and specialized statistical tools are required in their analysis. The methodology discussed in this work offers nonparametric tests that can detect differences in such data with greater power and good control of TypeI error over existing methods. The incorporation of Wavelet Transforms makes the test an efficient approach due to its decorrelation properties. These tests are designed primarily to handle functional responses from multiple treatments simultaneously and generally are extensible to high dimensional data. The sparseness introduced by Wavelet Transforms is another advantage of this test when compared to traditional tests. In addition to offering a theoretical framework, several applications of such tests in the fields of engineering, genomics and quantitative finance are also discussed.
Show less  Date Issued
 2014
 Identifier
 FSU_migr_etd8789
 Format
 Thesis
 Title
 Nonparametric Change Point Detection Methods for Profile Variability.
 Creator

Geneus, Vladimir J. (Vladimir Jacques), Chicken, Eric, Liu, Guosheng (Professor of Earth, Ocean and Atmospheric Science), Sinha, Debajyoti, Zhang, Xin (Professor of Engineering)...
Show moreGeneus, Vladimir J. (Vladimir Jacques), Chicken, Eric, Liu, Guosheng (Professor of Earth, Ocean and Atmospheric Science), Sinha, Debajyoti, Zhang, Xin (Professor of Engineering), Florida State University, College of Arts and Sciences, Department of Statistics
Show less  Abstract/Description

Due to the importance of seeing profile change in devices such as of medical apparatus, measuring the change point in variability of a different functions is important. In a sequence of functional observations (each of the same length), we wish to determine as quickly as possible when a change in the observations has occurred. Waveletbased change point methods are proposed that determine when the variability of the noise in a sequence of functional profiles (i.e. the precision profile of...
Show moreDue to the importance of seeing profile change in devices such as of medical apparatus, measuring the change point in variability of a different functions is important. In a sequence of functional observations (each of the same length), we wish to determine as quickly as possible when a change in the observations has occurred. Waveletbased change point methods are proposed that determine when the variability of the noise in a sequence of functional profiles (i.e. the precision profile of medical devices) has occurred; goes out of control from a known, fixed value, or an estimated incontrol value. Various methods have been proposed which focus on changes in the form of the function. One method, the NEWMA, based on EWMA, focuses on changes in both. However, the drawback is that the form of the incontrol function is known. Others methods, including the χ² for Phase I & Phase II make some assumption about the function. Our interest, however, is in detecting changes in the variance from one function to the next. In particular, we are interested not on differences from one profile to another (variance between), rather differences in variance (variance within). The functional portion of the profiles is allowed to come from a large class of functions and may vary from profile to profile. The estimator is evaluated on a variety of conditions, including allowing the wavelet noise subspace to be substantially contaminated by the profile's functional structure, and is compared to two competing noise monitoring methods. Nikoo and Noorossana (2013) propose a nonparametric wavelet regression method that uses both change point techniques to monitor the variance: a Nonparametric Control Charts, via the mean of m median control charts, and a Parametric Control Charts, via χ²distribution. We propose improvements to their method by incorporating prior data and making use of likelihood ratios. Our methods make use of the orthogonal properties of wavelet projections to accurately and efficiently monitor the level of noise from one profile to the next; detect changes in noise in Phase II setting. We show through simulation results that our proposed methods have better power and are more robust against the confounding effect between variance estimation and function estimation. The proposed methods are shown to be very efficient at detecting when the variability has changed through an extensive simulation study. Extensions are considered that explore the usage of windowing and estimated incontrol values for the MAD method; and the effect of the exact distribution under normality rather than the asymptotic distribution. These developments are implemented in the parametric, nonparametric scale, and complete nonparameric settings. The proposed methodologies are tested through simulation and applicable to various biometric and health related topics; and have the potential to improve in computational efficiency and in reducing the number of assumptions required.
Show less  Date Issued
 2017
 Identifier
 FSU_SUMMER2017_Geneus_fsu_0071E_13862
 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
 Nonparametric Detection of Arbitrary Changes to Distributions and Methods of Regularization of Piecewise Constant Functional Data.
 Creator

Orndorff, Mark Adam, Chicken, Eric, Liu, Guosheng, Pati, Debdeep, Tao, Minjing, Florida State University, College of Arts and Sciences, Department of Statistics
 Abstract/Description

Nonparametric statistical methods can refer a wide variety of techniques. In this dissertation, we focus on two problems in statistics which are common applications of nonparametric statistics. The main body of the dissertation focuses on distributionfree process control for detection of arbitrary changes to the distribution of an underlying random variable. A secondary problem, also part of the broad umbrella of nonparametric statistics, is the proper approximation of a function....
Show moreNonparametric statistical methods can refer a wide variety of techniques. In this dissertation, we focus on two problems in statistics which are common applications of nonparametric statistics. The main body of the dissertation focuses on distributionfree process control for detection of arbitrary changes to the distribution of an underlying random variable. A secondary problem, also part of the broad umbrella of nonparametric statistics, is the proper approximation of a function. Statistical process control minimizes disruptions to a properly controlled process and quickly terminates out of control processes. Although rarely satisfied in practice, strict distributional assumptions are often needed to monitor these processes. Previous models have often exclusively focused on monitoring changes in the mean or variance of the underlying process. The proposed model establishes a monitoring method requiring few distributional assumptions while monitoring all changes in the underlying distribution generating the data. No assumptions on the form of the incontrol distribution are made other than independence within and between observed samples. Windowing is employed to reduce computational complexity of the algorithm as well as ensure fast detection of changes. Results indicate quicker detection of large jumps than in many previously established methods. It is now common to analyze large quantities of data generated by sensors over time. Traditional analysis techniques do not incorporate the inherent functional structure often present in this type of data. The second focus of this dissertation is the development of a analysis method for functional data where the range of the function has a discrete, ordinal structure. Use is made of spline based methods using a piecewise constant function approximation. After a large amount of data reduction is achieved, generalized linear mixed model methodology is employed in order to model the data.
Show less  Date Issued
 2017
 Identifier
 FSU_2017SP_Orndorff_fsu_0071E_13820
 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
 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
 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
 Practical Methods for Equivalence and NonInferiority Studies with Survival Response.
 Creator

Martinez, Elvis Englebert, Sinha, Debajyoti, Levenson, Cathy W., Chicken, Eric, Lipsitz, Stuart, McGee, Daniel, Florida State University, College of Arts and Sciences,...
Show moreMartinez, Elvis Englebert, Sinha, Debajyoti, Levenson, Cathy W., Chicken, Eric, Lipsitz, Stuart, McGee, Daniel, Florida State University, College of Arts and Sciences, Department of Statistics
Show less  Abstract/Description

Determining the equivalence or noninferiority of a new drug (test drug) with a existing treatment (reference drug) is an important topic of statistical interest. Wellek (1993) pioneered the way for logrank based equivalence and noninferiority testing by formulating a testing procedure using proportional hazards model (PHM) of Cox (1972). In many equivalence and noninferiority trials, two hazards functions may converge to one rather than being proportional for all timepoints. In this case...
Show moreDetermining the equivalence or noninferiority of a new drug (test drug) with a existing treatment (reference drug) is an important topic of statistical interest. Wellek (1993) pioneered the way for logrank based equivalence and noninferiority testing by formulating a testing procedure using proportional hazards model (PHM) of Cox (1972). In many equivalence and noninferiority trials, two hazards functions may converge to one rather than being proportional for all timepoints. In this case, the proportional odds survival model (POSM) of Bennett (1983) will be more sufficient than a Cox's PHM assumption. We show in both cases, when the wrong modeling assumption is made and Cox's PH assumption is violated, the popular procedure of Wellek (1993) has an inflated type I error. On the contrary, our proposed POS model based equivalence and noninferiority tests maintains the practitioners desired 5% level of significance regardless of the underlying modeling assumption (e.g. Cox,1972; Wellek, 1993). Furthermore for noninferiority trials, we introduce a method to determine the optimal sample size required when a desired power and type I error is specified and the data follows the POSM of Bennett (1983). For both of the above trials, we present simulation studies showing the finite approximation of powers and type I error rates, when the underlying modeling assumption are correctly specified and when the assumptions are misspecified.
Show less  Date Issued
 2014
 Identifier
 FSU_migr_etd9214
 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
 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
 Scalable and Structured High Dimensional Covariance Matrix Estimation.
 Creator

Sabnis, Gautam, Pati, Debdeep, Kercheval, Alec N., Sinha, Debajyoti, Chicken, Eric, Florida State University, College of Arts and Sciences, Department of Statistics
 Abstract/Description

With rapid advances in data acquisition and storage techniques, modern scientific investigations in epidemiology, genomics, imaging and networks are increasingly producing challenging data structures in the form of highdimensional vectors, matrices and multiway arrays (tensors) rendering traditional statistical and computational tools inappropriate. One hope for meaningful inferences in such situations is to discover an inherent lowerdimensional structure that explains the physical or...
Show moreWith rapid advances in data acquisition and storage techniques, modern scientific investigations in epidemiology, genomics, imaging and networks are increasingly producing challenging data structures in the form of highdimensional vectors, matrices and multiway arrays (tensors) rendering traditional statistical and computational tools inappropriate. One hope for meaningful inferences in such situations is to discover an inherent lowerdimensional structure that explains the physical or biological process generating the data. The structural assumptions impose constraints that force the objects of interest to lie in lowerdimensional spaces, thereby facilitating their estimation and interpretation and, at the same time reducing computational burden. The assumption of an inherent structure, motivated by various scientific applications, is often adopted as the guiding light in the analysis and is fast becoming a standard tool for parsimonious modeling of such high dimensional data structures. The content of this thesis is specifically directed towards methodological development of statistical tools, with attractive computational properties, for drawing meaningful inferences though such structures. The third chapter of this thesis proposes a distributed computing framework, based on a divide and conquer strategy and hierarchical modeling, to accelerate posterior inference for highdimensional Bayesian factor models. Our approach distributes the task of highdimensional covariance matrix estimation to multiple cores, solves each subproblem separately via a latent factor model, and then combines these estimates to produce a global estimate of the covariance matrix. Existing divide and conquer methods focus exclusively on dividing the total number of observations n into subsamples while keeping the dimension p fixed. The approach is novel in this regard: it includes all of the n samples in each subproblem and, instead, splits the dimension p into smaller subsets for each subproblem. The subproblems themselves can be challenging to solve when p is large due to the dependencies across dimensions. To circumvent this issue, a novel hierarchical structure is specified on the latent factors that allows for flexible dependencies across dimensions, while still maintaining computational efficiency. Our approach is readily parallelizable and is shown to have computational efficiency of several orders of magnitude in comparison to fitting a full factor model. The fourth chapter of this thesis proposes a novel way of estimating a covariance matrix that can be represented as a sum of a lowrank matrix and a diagonal matrix. The proposed method compresses highdimensional data, computes the sample covariance in the compressed space, and lifts it back to the ambient space via a decompression operation. A salient feature of our approach relative to existing literature on combining sparsity and lowrank structures in covariance matrix estimation is that we do not require the lowrank component to be sparse. A principled framework for estimating the compressed dimension using Stein's Unbiased Risk Estimation theory is demonstrated. In the final chapter of this thesis, we tackle the problem of variable selection in high dimensions. Consistent model selection in high dimensions has received substantial interest in recent years and is an extremely challenging problem for Bayesians. The literature on model selection with continuous shrinkage priors is even lessdeveloped due to the unavailability of exact zeros in the posterior samples of parameter of interest. Heuristic methods based on thresholding the posterior mean are often used in practice which lack theoretical justification, and inference is highly sensitive to the choice of the threshold. We aim to address the problem of selecting variables through a novel method of post processing the posterior samples.
Show less  Date Issued
 2017
 Identifier
 FSU_SUMMER2017_Sabnis_fsu_0071E_14043
 Format
 Thesis
 Title
 Shape Constrained Single Index Models for Biomedical Studies.
 Creator

Dhara, Kumaresh, Sinha, Debajyoti, Pati, Debdeep, Proudfit, Greg Hajcak, Slate, Elizabeth H., Chicken, Eric, Florida State University, College of Arts and Sciences, Department...
Show moreDhara, Kumaresh, Sinha, Debajyoti, Pati, Debdeep, Proudfit, Greg Hajcak, Slate, Elizabeth H., Chicken, Eric, Florida State University, College of Arts and Sciences, Department of Statistics
Show less  Abstract/Description

For many biomedical, environmental and economic studies with an unknown nonlinear relationship between the response and its multiple predictors, a single index model provides practical dimension reduction and good physical interpretation. However widespread uses of existing Bayesian analysis for such models are lacking in biostatistics due to some major impediments including slow mixing of the Markov Chain Monte Carlo (MCMC), inability to deal with missing covariates and a lack of...
Show moreFor many biomedical, environmental and economic studies with an unknown nonlinear relationship between the response and its multiple predictors, a single index model provides practical dimension reduction and good physical interpretation. However widespread uses of existing Bayesian analysis for such models are lacking in biostatistics due to some major impediments including slow mixing of the Markov Chain Monte Carlo (MCMC), inability to deal with missing covariates and a lack of theoretical justification of the rate of convergence. We present a new Bayesian single index model with associated MCMC algorithm that incorporates an efficient Metropolis Hastings (MH) step for the conditional distribution of the index vector. Our method leads to a model with good biological interpretation and prediction, implementable Bayesian inference, fast convergence of the MCMC, and a first time extension to accommodate missing covariates. We also obtain for the first time, the set of sufficient conditions for obtaining the optimal rate of convergence of the overall regression function. We illustrate the practical advantages of our method and computational tool via reanalysis of an environmental study. I have proposed a frequentist and a Bayesian methods for a monotone singleindex models using the Bernstein polynomial basis to represent the link function. The monotonicity of the unknown link function creates a clinically interpretable index, along with the relative importance of the covariates on the index. We develop a computationallysimple, iterative, profile likelihoodbased method for the frequentist analysis. To ease the computational complexity of the Bayesian analysis, we also develop a novel and efficient MetropolisHastings step to sample from the conditional posterior distribution of the index parameters. These methodologies and their advantages over existing methods are illustrated via simulation studies. These methods are also used to analyze depression based measures among adolescent girls.
Show less  Date Issued
 2018
 Identifier
 2018_Su_Dhara_fsu_0071E_14739
 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
 Survival Analysis Using Bayesian Joint Models.
 Creator

Xu, Zhixing, Sinha, Debajyoti, Schatschneider, Christopher, Bradley, Jonathan R., Chicken, Eric, Lin, Lifeng, Florida State University, College of Arts and Sciences, Department...
Show moreXu, Zhixing, Sinha, Debajyoti, Schatschneider, Christopher, Bradley, Jonathan R., Chicken, Eric, Lin, Lifeng, Florida State University, College of Arts and Sciences, Department of Statistics
Show less  Abstract/Description

In many clinical studies, each patient is at risk of recurrent events as well as the terminating event. In Chapter 2, we present a novel latentclass based semiparametric joint model that offers clinically meaningful and estimable association between the recurrence profile and risk of termination. Unlike previous sharedfrailty based joint models, this model has a coherent interpretation of the covariate effects on all relevant functions and model quantities that are either conditional or...
Show moreIn many clinical studies, each patient is at risk of recurrent events as well as the terminating event. In Chapter 2, we present a novel latentclass based semiparametric joint model that offers clinically meaningful and estimable association between the recurrence profile and risk of termination. Unlike previous sharedfrailty based joint models, this model has a coherent interpretation of the covariate effects on all relevant functions and model quantities that are either conditional or unconditional on events history. We offer a fully Bayesian method for estimation and prediction using a complete specification of the prior process of the baseline functions. When there is a lack of prior information about the baseline functions, we derive a practical and theoretically justifiable partial likelihood based semiparametric Bayesian approach. Our Markov Chain Monte Carlo tools for both Bayesian methods are implementable via publicly available software. Practical advantages of our methods are illustrated via a simulation study and the analysis of a transplant study with recurrent NonFatal Graft Rejections (NFGR) and the termination event of death due to total graft rejection. In Chapter 3, we are motivated by the important problem of estimating Daily Fine Particulate Matter (PM2.5) over the US. Tracking and estimating Daily Fine Particulate Matter (PM2.5) is very important as it has been shown that PM2.5 is directly related to mortality related to the lungs, cardiovascular system, and stroke. That is, high values of PM2.5 constitute a public health problem in the US, and it is important that we precisely estimate PM2.5 to aid in public policy decisions. Thus, we propose a Bayesian hierarchical model for highdimensional ``multitype" responses. By ``multitype" responses we mean a collection of correlated responses that have different distributional assumptions (e.g., continuous skewed observations, and countvalued observations). The Centers for Disease Control and Prevention (CDC) database provides counts of mortalities related to PM2.5 and daily averaged PM2.5 which are treated as responses in our analysis. Our model capitalizes on the shared conjugate structure between the Weibull (to model PM2.5), Poisson (to model diseases mortalities), and multivariate loggamma distributions, and use dimension reduction to aid with computation. Our model can also be used to improve the precision of estimates and estimate at undisclosed/missing counties. We provide a simulation study to illustrate the performance of the model and give an indepth analysis of the CDC dataset.
Show less  Date Issued
 2019
 Identifier
 2019_Spring_Xu_fsu_0071E_15078
 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
 WaveletBased Bayesian Approaches to Sequential Profile Monitoring.
 Creator

Varbanov, Roumen, Chicken, Eric, Linero, Antonio Ricardo, Huffenberger, Kevin M., Yang, Yanyun, Florida State University, College of Arts and Sciences, Department of Statistics
 Abstract/Description

We consider changepoint detection and estimation in sequences of functional observations. This setting often arises when the quality of a process is characterized by such observations, termed profiles, and monitoring profiles for changes in structure can be used to ensure the stability of the process over time. While interest in profile monitoring has grown, few methods approach the problem from a Bayesian perspective. In this dissertation, we propose three waveletbased Bayesian approaches...
Show moreWe consider changepoint detection and estimation in sequences of functional observations. This setting often arises when the quality of a process is characterized by such observations, termed profiles, and monitoring profiles for changes in structure can be used to ensure the stability of the process over time. While interest in profile monitoring has grown, few methods approach the problem from a Bayesian perspective. In this dissertation, we propose three waveletbased Bayesian approaches to profile monitoring  the last of which can be extended to a general process monitoring setting. First, we develop a general framework for the problem of interest in which we base inference on the posterior distribution of the change point without placing restrictive assumptions on the form of profiles. The proposed method uses an analytic form of the posterior distribution in order to run online without relying on Markov chain Monte Carlo (MCMC) simulation. Wavelets, an effective tool for estimating nonlinear signals from noisecontaminated observations, enable the method to flexibly distinguish between sustained changes in profiles and the inherent variability of the process. Second, we modify the initial framework in a posterior approximation algorithm designed to utilize past information in a computationally efficient manner. We show that the approximation can detect changes of smaller magnitude better than traditional alternatives for curbing computational cost. Third, we introduce a monitoring scheme that allows an unchanged process to run infinitely long without a false alarm; the scheme maintains the ability to detect a change with probability one. We include theoretical results regarding these properties and illustrate the implementation of the scheme in the previously established framework. We demonstrate the efficacy of proposed methods on simulated data and significantly outperform a relevant frequentist competitor.
Show less  Date Issued
 2018
 Identifier
 2018_Sp_Varbanov_fsu_0071E_14513
 Format
 Thesis