Journal
STATISTICS AND COMPUTING
Volume 31, Issue 5, Pages -Publisher
SPRINGER
DOI: 10.1007/s11222-021-10042-6
Keywords
Bayesian inversion; Parallel tempering; Infinite swapping; Markov chain Monte Carlo; Uncertainty quantification
Funding
- King Abdullah University of Science and Technology (KAUST) Office of Sponsored Research (OSR) [URF/1/2281-01-01, URF/1/2584-01-01]
- Alexander von Humboldt Foundation
- Deutsche Forschungsgemeinschaft (DFG) through the TUM International Graduate School of Science and Engineering (IGSSE) [10.02 BAYES]
- Swiss Data Science Center (SDSC) [p18-09]
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In this work, two generalizations of the Parallel Tempering algorithm are introduced, with state-dependent swapping rates inspired by a continuous time Infinite Swapping algorithm. The analysis of reversibility and ergodicity properties show that these generalized PT algorithms significantly improve sampling efficiency compared to more traditional sampling algorithms.
In the current work we present two generalizations of the Parallel Tempering algorithm in the context of discrete-timeMarkov chainMonteCarlo methods for Bayesian inverse problems. These generalizations use state-dependent swapping rates, inspired by the so-called continuous time Infinite Swapping algorithm presented in Plattner et al. (J Chem Phys 135(13):134111, 2011). We analyze the reversibility and ergodicity properties of our generalized PT algorithms. Numerical results on sampling from different target distributions, show that the proposed methods significantly improve sampling efficiency over more traditional sampling algorithms such as Random Walk Metropolis, preconditioned Crank-Nicolson, and (standard) Parallel Tempering.
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