Open Collections

Lee, Gahyung (Seren)

University of British Columbia

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).

Text

2025-04-23

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/90745

Statistics

University of British Columbia

UBCV

http://creativecommons.org/licenses/by-nc-nd/4.0/