Generalized parallel tempering on Bayesian inverse problems

Abstract In the current work we present two generalizations of Parallel Tempering algorithm in context discrete-time Markov chain Monte Carlo methods for Bayesian inverse problems. These use state-dependent swapping rates, inspired by so-called continuous time Infinite Swapping presented Plattner et al. (J Chem Phys 135(13):134111, 2011). We analyze reversibility and ergodicity properties our generalized PT algorithms. Numerical results on sampling from different target distributions, show that proposed significantly improve efficiency over more traditional algorithms such as Random Walk Metropolis, preconditioned Crank–Nicolson, (standard) Tempering.