2009/03/31 by Matti Vihola · 1 citation
Mathematics · Physics and Astronomy · #Algorithm #Applied mathematics #Combinatorics #Computer science #Covariance #Ergodic theory #Ergodicity #Interval (graph theory) #Markov Chains and Monte Carlo Methods #Markov chain Monte Carlo #Mathematical analysis #Mathematics #Metropolis–Hastings algorithm #Monte Carlo method #Random walk #Scaling #Stability (learning theory) #Statistical physics #Statistics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math.PR #math.ST #msc:60J27 #msc:65C40 #msc:93E15 #msc:93E35 #stat.TH
paper · pdf · doi:10.1016/j.spa.2011.08.006
published as Stochastic Processes and their Applications 121(12):2839-2860, 2011 · 24 pages, 1 figure; major revision
arxiv created 2011/04/05 · openalex publication_date 2011/08/25 · arxiv updated 2011/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The stability and ergodicity properties of two adaptive random walk Metropolis algorithms are considered. The both algorithms adjust the scaling of the proposal distribution continuously based on the observed acceptance probability. Unlike the previously proposed forms of the algorithms, the adapted scaling parameter is not constrained within a predefined compact interval. The first algorithm is based on scale adaptation only, while the second one incorporates also covariance adaptation. A strong law of large numbers is shown to hold assuming that the target density is smooth enough and has either compact support or super-exponentially decaying tails.