Convergence of adaptive and interacting Markov chain Monte Carlo algorithms

Abstract

Adaptive and interacting Markov chain Monte Carlo algorithms (MCMC) have been recently introduced in the literature. These novel simulation algorithms are designed to increase the simulation efficiency to sample complex distributions. Motivated by some recently introduced algorithms (such as the adaptive Metropolis algorithm and the interacting tempering algorithm), we develop a general methodological and theoretical framework to establish both the convergence of the marginal distribution and a strong law of large numbers. This framework weakens the conditions introduced in the pioneering paper by Roberts and Rosenthal [J. Appl. Probab. 44 (2007) 458--475]. It also covers the case when the target distribution $\pi$ is sampled by using Markov transition kernels with a stationary distribution that differs from $\pi$.

Published in at http://dx.doi.org/10.1214/11-AOS938 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (5)

• Renewal theory and computable convergence rates for geometrically ergodic Markov chains
• Quantitative bounds on convergence of time-inhomogeneous Markov chains
• Convergence of adaptive and interacting Markov chain Monte Carlo algorithms
• Sequentially interacting Markov chain Monte Carlo methods
• On nonlinear Markov chain Monte Carlo

Cited by in corpus (6)

• Convergence of adaptive and interacting Markov chain Monte Carlo algorithms
• Adaptive parallel tempering algorithm
• Adaptive Equi-Energy Sampler : Convergence and Illustration
• Self-Healing Umbrella Sampling: Convergence and efficiency
• Adaptive Markov Chain Monte Carlo for Auxiliary Variable Method and Its Application to Parallel Tempering
• Forgetting the starting distribution in finite interacting tempering