On the geometric ergodicity of Metropolis-Hastings algorithms

DOI10.1080/10485250601033214zbMath1131.65004OpenAlexW1965943102MaRDI QIDQ5429699

François Perron, Yves F. Atchadé

Publication date: 3 December 2007

Published in: Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10485250601033214

zbMATH Keywords

global stabilityMetropolis-Hastings algorithmgeometric ergodicityMarkov chain operatorMonte Carlo estimationindependent Metropolis-Hastings algorithm

Mathematics Subject Classification ID

Computational methods in Markov chains (60J22) Monte Carlo methods (65C05) Numerical analysis or methods applied to Markov chains (65C40) Continuous-time Markov processes on discrete state spaces (60J27) Transition functions, generators and resolvents (60J35)

Related Items (10)

Approximate Bayesian computation by modelling summary statistics in a quasi-likelihood framework ⋮ Exact convergence analysis of the independent Metropolis-Hastings algorithms ⋮ A computable bound of the essential spectral radius of finite range metropolis-Hastings kernels ⋮ Multiplicative random walk Metropolis-Hastings on the real line ⋮ Nonasymptotic Bounds on the Mean Square Error for MCMC Estimates via Renewal Techniques ⋮ Convergence rate of multiple-try Metropolis independent sampler ⋮ Explicit bounds for spectral theory of geometrically ergodic Markov kernels and applications ⋮ Deterministic and stochastic damage detection via dynamic response analysis ⋮ Error Bounds for Dynamical Spectral Estimation ⋮ Exact MCMC with differentially private moves. Exact MCMC with differentially private moves, revisiting the penalty algorithm in a data privacy framework

Cites Work

• Markov chains and stochastic stability
• General state space Markov chains and MCMC algorithms
• On the Markov chain central limit theorem
• Markov chains for exploring posterior distributions. (With discussion)
• Rates of convergence of the Hastings and Metropolis algorithms
• Geometric L² and ^{L1 convergence are equivalent for reversible Markov chains}
• Geometric convergence and central limit theorems for multidimensional Hastings and Metropolis algorithms
• Markov-chain monte carlo: Some practical implications of theoretical results

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