Academic Journal
Generating MCMC proposals by randomly rotating the regular simplex
| Title: | Generating MCMC proposals by randomly rotating the regular simplex |
|---|---|
| Authors: | Andrew J. Holbrook |
| Source: | J Multivar Anal |
| Publication Status: | Preprint |
| Publisher Information: | Elsevier BV, 2023. |
| Publication Year: | 2023 |
| Subject Terms: | Haar measure, FOS: Computer and information sciences, Other Statistics (stat.OT), Monte Carlo methods, 02 engineering and technology, parallel MCMC, Statistics - Computation, 01 natural sciences, Article, Markov chain Monte Carlo, Statistics - Other Statistics, 0202 electrical engineering, electronic engineering, information engineering, Numerical analysis or methods applied to Markov chains, 0101 mathematics, Computational methods for problems pertaining to statistics, Computation (stat.CO), orthogonal group |
| Description: | We present the simplicial sampler, a class of parallel MCMC methods that generate and choose from multiple proposals at each iteration. The algorithm's multiproposal randomly rotates a simplex connected to the current Markov chain state in a way that inherently preserves symmetry between proposals. As a result, the simplicial sampler leads to a simplified acceptance step: it simply chooses from among the simplex nodes with probability proportional to their target density values. We also investigate a multivariate Gaussian-based symmetric multiproposal mechanism and prove that it also enjoys the same simplified acceptance step. This insight leads to significant theoretical and practical speedups. While both algorithms enjoy natural parallelizability, we show that conventional implementations are sufficient to confer efficiency gains across an array of dimensions and a number of target distributions. To appear in Journal of Multivariate Analysis. Code here: https://github.com/andrewjholbrook/simplicialSampler |
| Document Type: | Article Other literature type |
| File Description: | application/xml |
| Language: | English |
| ISSN: | 0047-259X |
| DOI: | 10.1016/j.jmva.2022.105106 |
| DOI: | 10.48550/arxiv.2110.06445 |
| Access URL: | https://pubmed.ncbi.nlm.nih.gov/37799825 http://arxiv.org/abs/2110.06445 https://zbmath.org/7636963 https://doi.org/10.1016/j.jmva.2022.105106 |
| Rights: | CC BY NC ND arXiv Non-Exclusive Distribution URL: http://creativecommons.org/licenses/by-nc-nd/4.0/This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/ (http://creativecommons.org/licenses/by-nc-nd/4.0/) ). |
| Accession Number: | edsair.doi.dedup.....91e87183e77bd2cb0ed4ceb9d585d7c7 |
| Database: | OpenAIRE |
| ISSN: | 0047259X |
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| DOI: | 10.1016/j.jmva.2022.105106 |