@article{ab78c5fb87aa4d5fb5bebcbca47074d4,

title = "A Repelling–Attracting Metropolis Algorithm for Multimodality",

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.",

author = "Hyungsuk Tak and Meng, {Xiao Li} and {van Dyk}, {David A.}",

note = "Funding Information: This project was conducted under the auspices of the CHASC International Astrostatistics Center. CHASC is supported by the NSF grants DMS 1208791, 1209232, 1513484, 1513492, and 1513546. Xiao-Li Meng acknowledges partial financial support from the NSF grants given to CHASC. Hyungsuk Tak acknowledges partial support from the NSF grants DMS 1127914 and 1638521 given to SAMSI. David A. van Dyk acknowledges support from a Wolfson Research Merit Award (WM110023) provided by the British Royal Society and from a Marie-Curie Career Integration Grant (FP7-PEOPLE-2012-CIG-321865) provided by the European Commission. The authors thank the associate editor and two referees for their insightful comments and suggestions that significantly improved the presentation. We also thank Christian P. Robert, Pierre E. Jacob, Art B. Owen, and Natesh S. Pillai for very helpful discussions and Steven R. Finch for his proofreading. Funding Information: National Science Foundation [DMS 1127914, DMS 1208791, DMS 1209232, DMS 1513484, DMS 1513492, DMS 1513546, DMS 1638521]; Wolfson Research Merit Award [WM110023]; Marie-Curie Career Integration [FP7-PEOPLE-2012-CIG-321865] This project was conducted under the auspices of the CHASC International Astrostatistics Center. CHASC is supported by the NSF grants DMS 1208791, 1209232, 1513484, 1513492, and 1513546. Xiao-Li Meng acknowledges partial financial support from the NSF grants given to CHASC. Hyungsuk Tak acknowledges partial support from the NSF grants DMS 1127914 and 1638521 given to SAMSI. David A. van Dyk acknowledges support from a Wolfson Research Merit Award (WM110023) provided by the British Royal Society and from a Marie-Curie Career Integration Grant (FP7-PEOPLE-2012-CIG-321865) provided by the European Commission. The authors thank the associate editor and two referees for their insightful comments and suggestions that significantly improved the presentation. We also thank Christian?P.?Robert, Pierre?E.?Jacob, Art?B.?Owen, and Natesh?S.?Pillai for very helpful discussions and Steven R. Finch for his proofreading. Funding Information: National Science Foundation [DMS 1127914, DMS 1208791, DMS 1209232, DMS 1513484, DMS 1513492, DMS 1513546, DMS 1638521]; Wolfson Research Merit Award [WM110023]; Marie-Curie Career Integration [FP7-PEOPLE-2012-CIG-321865] Publisher Copyright: {\textcopyright} 2018, {\textcopyright} 2018 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America.",

year = "2018",

month = jul,

day = "3",

doi = "10.1080/10618600.2017.1415911",

language = "English (US)",

volume = "27",

pages = "479--490",

journal = "Journal of Computational and Graphical Statistics",

issn = "1061-8600",

publisher = "American Statistical Association",

number = "3",

}