Adaptive Incremental Mixture Markov chain Monte Carlo

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Title: Adaptive Incremental Mixture Markov chain Monte Carlo
Authors: Marie, FlorianFriel, NialMira, AntoniettaRaftery, 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 MCMCBayesian inferenceIndependence SamplerImportance weightLocal adaptation
DOI: 10.1080/10618600.2019.1598872
Language: en
Status of Item: Peer reviewed
Appears in Collections:Insight Research Collection

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