A repelling–attracting metropolis algorithm for multimodality
File(s)
Accepted version
Author(s)
Tak, Hyungsuk
Meng, Xiao-Li
van Dyk, David
Type
Journal Article
Abstract
Although the Metropolis algorithm is simple to implement, it often has difficulties exploring multimodal distributions. We propose the repelling–attracting Metropolis (RAM) algorithm that maintains the simple-to-implement nature of the Metropolis algorithm, but is more likely to jump between modes. The RAM algorithm is a Metropolis-Hastings algorithm with a proposal that consists of a downhill move in density that aims to make local modes repelling, followed by an uphill move in density that aims to make local modes attracting. The downhill move is achieved via a reciprocal Metropolis ratio so that the algorithm prefers downward movement. The uphill move does the opposite using the standard Metropolis ratio which prefers upward movement. This down-up movement in density increases the probability of a proposed move to a different mode. Because the acceptance probability of the proposal involves a ratio of intractable integrals, we introduce an auxiliary variable which creates a term in the acceptance probability that cancels with the intractable ratio. Using several examples, we demonstrate the potential for the RAM algorithm to explore a multimodal distribution more efficiently than a Metropolis algorithm and with less tuning than is commonly required by tempering-based methods. Supplementary materials are available online.
Date Issued
2018-07-03
Date Acceptance
2017-11-24
Citation
Journal of Computational and Graphical Statistics, 2018, 27 (3), pp.479-490
ISSN
1061-8600
Publisher
Taylor & Francis
Start Page
479
End Page
490
Journal / Book Title
Journal of Computational and Graphical Statistics
Volume
27
Issue
3
Replaces
10044/1/62943
Copyright Statement
© 2018 Taylor & Francis. This is an Accepted Manuscript of an article published by Taylor & Francis in Journal of Computational and Graphical Statistics on 3rd July 2018, available online: https://doi.org/10.1080/10618600.2017.1415911
Sponsor
The Royal Society
Commission of the European Communities
National Science Foundation (US)
Commission of the European Communities
Grant Number
WM110023
FP7-PEOPLE-2012-CIG-321865
DMS 15-13484
691164
Subjects
stat.ME
0104 Statistics
Statistics & Probability
Publication Status
Published
Date Publish Online
2018-07-18