Liang, Xitong;
Griffin, Jim;
Livingstone, sam;
(2022)
Adaptive random neighbourhood informed Markov chain Monte Carlo for high-dimensional Bayesian variable selection.
Statistics and Computing
, 32
, Article 84. 10.1007/s11222-022-10137-8.
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Abstract
We introduce a framework for efficient Markov chain Monte Carlo algorithms targeting discrete-valued high-dimensional distributions, such as posterior distributions in Bayesian variable selection problems. We show that many recently introduced algorithms, such as the locally informed sampler of Zanella (J Am Stat Assoc 115(530):852–865, 2020), the locally informed with thresholded proposal of Zhou et al. (Dimension-free mixing for high-dimensional Bayesian variable selection, 2021) and the adaptively scaled individual adaptation sampler of Griffin et al. (Biometrika 108(1):53–69, 2021), can be viewed as particular cases within the framework. We then describe a novel algorithm, the adaptive random neighbourhood informed sampler, which combines ideas from these existing approaches. We show using several examples of both real and simulated data-sets that a computationally efficient point-wise implementation (PARNI) provides more reliable inferences on a range of variable selection problems, particularly in the very large p setting.
| Type: | Article |
|---|---|
| Title: | Adaptive random neighbourhood informed Markov chain Monte Carlo for high-dimensional Bayesian variable selection |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s11222-022-10137-8 |
| Publisher version: | https://doi.org/10.1007/s11222-022-10137-8 |
| Language: | English |
| Additional information: | Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
| UCL classification: | UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > UCL School of Management UCL > Provost and Vice Provost Offices > UCL BEAMS UCL |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10154045 |
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