Generalized parallel tempering on Bayesian inverse problems

Statistics and Computing, vol. 31

Abstract

Abstract In the current work we present two generalizations of the Parallel Tempering algorithm in the context of discrete-time Markov chain Monte Carlo 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.

Authors 4

1. Jonas Latz

   University of Cambridge

   Affiliation as printed

   Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK

2. Juan P. Madrigal-Cianci corresponding

   École Polytechnique Fédérale de Lausanne

   Affiliation as printed

   SB-MATH-CSQI, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

3. Fabio Nobile

   École Polytechnique Fédérale de Lausanne

   Affiliation as printed

   SB-MATH-CSQI, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

4. Raul F. Tempone Aachen

   King Abdullah University of Science and Technology · RWTH Aachen University

   Affiliation as printed

   Alexander von Humboldt professor in Mathematics of Uncertainty Quantification, RWTH Aachen University, Aachen, Germany

   Computer, Electrical and Mathematical Sciences and Engineering, KAUST, Thuwal, Saudi Arabia