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Generalized parallel tempering on Bayesian inverse problems

Published version
Peer-reviewed

Change log

Authors

Latz, J 
Madrigal-Cianci, JP  ORCID logo  https://orcid.org/0000-0003-0398-2508
Nobile, F 
Tempone, R 

Abstract

In the current work we present two generalizations of the Parallel Tempering algorithm, inspired by the so-called continuous-time Infinite Swapping algorithm. Such a method, found its origins in the molecular dynamics community, and can be understood as the limit case of the continuous-time Parallel Tempering algorithm, where the (random) time between swaps of states between two parallel chains goes to zero. Thus, swapping states between chains occurs continuously. In the current work, we extend this idea to the context of time-discrete Markov chains and present two Markov chain Monte Carlo algorithms that follow the same paradigm as the continuous-time infinite swapping procedure. We analyze the convergence properties of such discrete-time algorithms in terms of their spectral gap, and implement them to sample from different target distributions. Numerical results show that the proposed methods significantly improve over more traditional sampling algorithms such as Random Walk Metropolis and (traditional) Parallel Tempering.

Description

Funder: Alexander von Humboldt-Stiftung; doi: http://dx.doi.org/10.13039/100005156

Keywords

math.NA, math.NA, cs.NA, stat.CO, 60J22, 60J20, 62F15, 65C05

Journal Title

Statistics and Computing

Conference Name

Journal ISSN

0960-3174
1573-1375

Volume Title

31

Publisher

Springer Science and Business Media LLC
Sponsorship
King Abdullah University of Science and Technology (URF/1/2281-01-01, URF/1/2584-01-01)
Graduate School, Technische Universität München (10.02 BAYES)
Swiss Data Science Center (p18-09)