On the ergodicity of the adaptive Metropolis algorithm on unbounded domains

Abstract

This paper describes sufficient conditions to ensure the correct ergodicity of the Adaptive Metropolis (AM) algorithm of Haario, Saksman and Tamminen [Bernoulli 7 (2001) 223--242] for target distributions with a noncompact support. The conditions ensuring a strong law of large numbers require that the tails of the target density decay super-exponentially and have regular contours. The result is based on the ergodicity of an auxiliary process that is sequentially constrained to feasible adaptation sets, independent estimates of the growth rate of the AM chain and the corresponding geometric drift constants. The ergodicity result of the constrained process is obtained through a modification of the approach due to Andrieu and Moulines [Ann. Appl. Probab. 16 (2006) 1462--1505].

Published in at http://dx.doi.org/10.1214/10-AAP682 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (3)

• On the ergodicity properties of some adaptive MCMC algorithms
• Renewal theory and computable convergence rates for geometrically ergodic Markov chains
• On the ergodicity of the adaptive Metropolis algorithm on unbounded domains

Cited by in corpus (23)

• Dimension-independent likelihood-informed MCMC
• Convergence of adaptive and interacting Markov chain Monte Carlo algorithms
• On the ergodicity of the adaptive Metropolis algorithm on unbounded domains
• Convergence properties of pseudo-marginal Markov chain Monte Carlo algorithms
• On perturbed proximal gradient algorithms
• Adaptive Gibbs samplers and related MCMC methods
• On the stability and ergodicity of adaptive scaling Metropolis algorithms
• Analysis of nonsmooth stochastic approximation: the differential inclusion approach
• Kernel estimators of asymptotic variance for adaptive Markov chain Monte Carlo
• Markovian stochastic approximation with expanding projections
• Grapham: Graphical Models with Adaptive Random Walk Metropolis Algorithms
• Bayesian computation: a perspective on the current state, and sampling backwards and forwards
• Accelerated dimension-independent adaptive Metropolis
• Stability of adversarial Markov chains, with an application to adaptive MCMC algorithms
• Adaptive parallel tempering algorithm
• On the stability of some controlled Markov chains and its applications to stochastic approximation with Markovian dynamic
• Almost sure convergence rates of adaptive increasingly rare Markov chain Monte Carlo
• On infinite-dimensional hierarchical probability models in statistical inverse problems
• On an adaptive preconditioned Crank-Nicolson MCMC algorithm for infinite dimensional Bayesian inferences
• Finite Sample Properties of Adaptive Markov Chains via Curvature
• Can the Adaptive Metropolis Algorithm Collapse Without the Covariance Lower Bound?
• Accelerating MCMC Algorithms
• Robust adaptive Metropolis algorithm with coerced acceptance rate