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Intensity Estimation in Poisson Processes with Phase Variability

Title: Intensity Estimation in Poisson Processes with Phase Variability.
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Name(s): Gordon, Glenna, author
Wu, Wei, professor directing dissertation
Whyte, James, IV, university representative
Srivastava, Anuj, 1968--, committee member
Chicken, Eric, committee member
Florida State University, degree granting institution
College of Arts and Sciences, degree granting college
Department of Statistics, degree granting department
Type of Resource: text
Genre: Text
Issuance: monographic
Date Issued: 2016
Publisher: Florida State University
Place of Publication: Tallahassee, Florida
Physical Form: computer
online resource
Extent: 1 online resource (106 pages)
Language(s): English
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 result, these estimation methods can yield estimators that are inefficient or that under-perform 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 alignment-based framework for intensity estimation. First, it is shown that the intensity function is area-preserved 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.
Identifier: FSU_FA2016_Gordon_fsu_0071E_13511 (IID)
Submitted Note: A Dissertation submitted to the Department of Statistics in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
Degree Awarded: Fall Semester 2016.
Date of Defense: October 7, 2016.
Keywords: emergency department utilization, functional data analysis, function registration, intensity estimation, Poisson process, spike train
Bibliography Note: Includes bibliographical references.
Advisory Committee: Wei Wu, Professor Directing Dissertation; James Whyte, IV, University Representative; Anuj Srivastava, Committee Member; Eric Chicken, Committee Member.
Subject(s): Statistics
Persistent Link to This Record: http://purl.flvc.org/fsu/fd/FSU_FA2016_Gordon_fsu_0071E_13511
Owner Institution: FSU

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Gordon, G. (2016). Intensity Estimation in Poisson Processes with Phase Variability. Retrieved from http://purl.flvc.org/fsu/fd/FSU_FA2016_Gordon_fsu_0071E_13511