Adaptive Incremental Mixture Markov chain Monte Carlo
|Title:||Adaptive Incremental Mixture Markov chain Monte Carlo||Authors:||Marie, Florian; Friel, Nial; Mira, Antonietta; Raftery, Adrian E.||Permanent link:||http://hdl.handle.net/10197/10865||Date:||7-Jun-2019||Online since:||2019-07-09T11:11:44Z||Abstract:||We propose Adaptive Incremental Mixture Markov chain Monte Carlo (AIMM), a novel approach to sample from challenging probability distributions defined on a general state-space. While adaptive MCMC methods usually update a parametric proposal kernel with a global rule, AIMM locally adapts a semiparametric kernel. AIMM is based on an independent Metropolis-Hastings proposal distribution which takes the form of a finite mixture of Gaussian distributions. Central to this approach is the idea that the proposal distribution adapts to the target by locally adding a mixture component when the discrepancy between the proposal mixture and the target is deemed to be too large. As a result, the number of components in the mixture proposal is not fixed in advance. Theoretically, we prove that there exists a process that can be made arbitrarily close to AIMM and that converges to the correct target distribution. We also illustrate that it performs well in practice in a variety of challenging situations, including high-dimensional and multimodal target distributions.||Funding Details:||Science Foundation Ireland||Type of material:||Journal Article||Publisher:||Taylor & Francis||Journal:||Journal of Computational and Graphical Statistics||Start page:||1||End page:||16||Copyright (published version):||2019 the Authors||Keywords:||Adaptive MCMC; Bayesian inference; Independence Sampler; Importance weight; Local adaptation||DOI:||10.1080/10618600.2019.1598872||Language:||en||Status of Item:||Peer reviewed|
|Appears in Collections:||Insight Research Collection|
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