Generalized parallel tempering on Bayesian inverse problems

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.

Automated summary

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.