Statistical models that are known or suspected to be partially identified : issues of parameterization, computation, and software development
department or school: Science, Faculty of
department or school: Statistics, Department of
data provider: DSpace
degree campus: UBCV
creator: Lee, Gahyung (Seren)
issued: 2025-04-23T21:29:20Z
issued: 2025
related degree: Doctor of Philosophy - PhD
degree grantor: University of British Columbia
description: With skyrocketing improvements in the performance of modern computing machines, the area of Bayesian inference applications is much improved, and Bayesian statistical analysis is used more frequently. In Bayesian inference, most computational resources are applied to running Markov chain Monte Carlo (MCMC) algorithms to obtain samples from posterior distributions. The MCMC algorithm is the main route to implement Bayesian inference. It allows for high-dimensional and flexible sampling. However, at the same time, researchers can experience poorer computational performance when Bayesian statistical inference is performed using a specific family of models, namely partially identified models. This is because the good computational performance of the MCMC algorithm is not guaranteed. The parameters of the partially identified model are not uniquely identified, which can make off-the-shelf MCMC algorithms very inefficient. Importance sampling with transparent reparameterization (ISTP) is a good computational remedy for posterior inference with partially identified models. With the ISTP algorithm, researchers can obtain better and more stable computational performance while still obtaining samples in the original parameterization. In this thesis, we first traverse scenarios of worsening computational performance with partially identified models and compare the results of ISTP with an off-the-shelf MCMC algorithm (Chapter 2). Then, we discuss the general usability of ISTP and develop the diagnostic method for models suspected to have partial or weak identification (Chapter 3). Along with ISTP, we introduce an R package for the Bayesian inference with the partially identified model (Chapter 4). Lastly, we discuss what was completed, its limitations, and possible future improvements (Chapter 5).
aggregated CHO: https://circle.library.ubc.ca/rest/handle/2429/90745
note: Statistical models that are known or suspected to bepartially identified: Issues of parameterization,computation, and software developmentbyGahyung (Seren) LeeB.Sc, The University of British Columbia, 2020A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFDoctor of PhilosophyinTHE FACULTY OF GRADUATE AND POSTDOCTORALSTUDIES(Statistics)The University of British Columbia(Vancouver)April 2025© Gahyung (Seren) Lee, 2025The following individuals certify that they have read, and recommend to the Fac-ulty of Graduate and Postdoctoral Studies for acceptance, the thesis entitled:Statistical models that are known or suspected to be partially identified:Issues of parameterization, computation, and software developmentsubmitted by Gahyung (Seren) Lee in partial fulfillment of the requirements forthe degree of Doctor of Philosophy in Statistics.Examining Committee:Paul Gustafson, Professor, Department of Statistics, UBCSupervisorAlexandre Bouchard-CoËte´, Professor, Department of Statistics, UBCSupervisory Committee MemberYongjin Park, Assistant Professor, Department of Statistics, UBCSupervisory Committee MemberDaniel J. McDonald , Associate Professor, Department of Statistics, UBCUniversity ExaminerKyungchul (Kevin) Song , Professor, Vancouver School of Economics, UBCUniversity ExaminerSaman Muthukumarana, Professor, Department of Statistics, University of Mani-tobaExternal ExamineriiAbstractWith skyrocketing improvements in the performance of modern computing ma-chines, the area of Bayesian inference applications is much improved, andBayesian statistical analysis is used more frequently. In Bayesian inference,most computational resources are applied to running Markov chain Monte Carlo(MCMC) algorithms to obtain samples from posterior distributions. The MCMCalgorithm is the main route to implement Bayesian inference. It allows for high-dimensional and flexible sampling. However, at the same time, researchers canexperience poorer computational perfo…
has type: Thesis/Dissertation
date issued: 2025-05
is shown at: 10.14288/1.0448519
language: eng
degree discipline: Statistics
provider: Vancouver : University of British Columbia Library
publisher: University of British Columbia
rights: Attribution-NonCommercial-NoDerivatives 4.0 International
rights URI: http://creativecommons.org/licenses/by-nc-nd/4.0/
scholar level: Graduate
contributor: Gustafson, Paul, 1968-
type: Text
identifier URI: http://hdl.handle.net/2429/90745