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Generating MCMC proposals by randomly rotating the regular simplex

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  • Holbrook, Andrew J.

Abstract

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.

Suggested Citation

  • Holbrook, Andrew J., 2023. "Generating MCMC proposals by randomly rotating the regular simplex," Journal of Multivariate Analysis, Elsevier, vol. 194(C).
    • Handle: RePEc:eee:jmvana:v:194:y:2023:i:c:s0047259x22000975
    DOI: 10.1016/j.jmva.2022.105106
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    References listed on IDEAS

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    1. Xin Luo & Håkon Tjelmeland, 2019. "A multiple-try Metropolis–Hastings algorithm with tailored proposals," Computational Statistics, Springer, vol. 34(3), pages 1109-1133, September.
    2. Bédard, Mylène & Douc, Randal & Moulines, Eric, 2012. "Scaling analysis of multiple-try MCMC methods," Stochastic Processes and their Applications, Elsevier, vol. 122(3), pages 758-786.
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