Liang, Xitong;
(2025)
Efficient Markov Chain Monte Carlo Algorithms for Bayesian Variable Selection.
Doctoral thesis (Ph.D), UCL (University College London).
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Abstract
Efficient Markov Chain Monte Carlo (MCMC) algorithms designed for discrete-valued high-dimensional distributions, such as posterior distributions arising in Bayesian variable selection (BVS) problems, are gaining increasing attention. This thesis aims to develop a series of novel efficient MCMC algorithms designed to address the challenges in discrete-valued high-dimensional distributions. I show that many existing MCMC schemes for discrete distributions, such as the locally informed proposals of Zanella (2020) and the Adaptively Scaled Individual Adaptation proposal (ASI) of Griffin et al. (2021), can be viewed as specific examples within a broader framework of random neighbourhood proposals. Based on this framework, I propose a new class of random neighbourhood-informed proposals where locally informed second-stage proposals are generated based on randomly constructed neighbourhoods. Using this framework, I develop the Adaptive Random Neighbourhood Informed (ARNI) proposal and point-wise implementation of ARNI (PARNI) proposal for learning the posterior distribution of the indicator variables obtained from Bayesian variable selection problems in linear and generalised linear models. Through several example real and simulated data-sets, I show that the PARNI proposal provides more reliable inferences on a range of variable selection problems, especially in high-dimensional settings. Furthermore, I extend the PARNI proposal to other discrete problems, including the Bayesian structure learning problem. The PARNI proposal continues to exhibit superior performance over other state-of-the-art algorithms in these applications, highlighting its high computational efficiency and robustness across different posterior distributions from discrete Bayesian inference problems.
| Type: | Thesis (Doctoral) |
|---|---|
| Qualification: | Ph.D |
| Title: | Efficient Markov Chain Monte Carlo Algorithms for Bayesian Variable Selection |
| Open access status: | An open access version is available from UCL Discovery |
| Language: | English |
| Additional information: | Copyright © The Author 2025. Original content in this thesis is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) Licence (https://creativecommons.org/licenses/by-nc/4.0/). Any third-party copyright material present remains the property of its respective owner(s) and is licensed under its existing terms. Access may initially be restricted at the author’s request. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10209134 |
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