Spectral gaps and error estimates for infinite-dimensional Metropolis-Hastings with non-Gaussian priors

DOI10.1214/22-aap1854zbMath1515.65012arXiv1810.00297OpenAlexW2982315231MaRDI QIDQ6104013

James E. Johndrow, Bamdad Hosseini

Publication date: 5 June 2023

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.00297

zbMATH Keywords

Markov chain Monte Carlospectral gapBayesian inverse problemnon-Gaussianweak Harris' theorem

Mathematics Subject Classification ID

Random fields; image analysis (62M40) Monte Carlo methods (65C05) Discrete-time Markov processes on general state spaces (60J05) Nonparametric inference (62G99)

Cites Work

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• Diffusion limits of the random walk Metropolis algorithm in high dimensions
• Besov priors for Bayesian inverse problems
• Spectral gaps for a Metropolis-Hastings algorithm in infinite dimensions
• Geometric analysis for the Metropolis algorithm on Lipschitz domains
• Asymptotic coupling and a general form of Harris' theorem with applications to stochastic delay equations
• Large data and zero noise limits of graph-based semi-supervised learning algorithms
• Micro-local analysis for the Metropolis algorithm
• What do we know about the Metropolis algorithm?
• Geometric ergodicity of Metropolis algorithms
• Perturbation theory for Markov chains via Wasserstein distance
• Spectral theory and limit theorems for geometrically ergodic Markov processes
• Rates of convergence of the Hastings and Metropolis algorithms
• Geometric ergodicity and the spectral gap of non-reversible Markov chains
• Fast mixing of Metropolis-Hastings with unimodal targets
• Well-posed Bayesian inverse problems and heavy-tailed stable quasi-Banach space priors
• A Liapounov bound for solutions of the Poisson equation
• Inverse problems: A Bayesian perspective
• Yet Another Look at Harris’ Ergodic Theorem for Markov Chains
• Refined generalizations of the triangle inequality on Banach spaces
• Convergence of Numerical Time-Averaging and Stationary Measures via Poisson Equations
• Uncertainty Quantification and Weak Approximation of an Elliptic Inverse Problem
• Studying Convergence of Markov Chain Monte Carlo Algorithms Using Coupled Sample Paths
• Uncertainty Quantification in Graph-Based Classification of High Dimensional Data
• Markov Chains and Stochastic Stability
• Geometric convergence and central limit theorems for multidimensional Hastings and Metropolis algorithms
• Ten Lectures on Wavelets
• Markov Chains
• Well-Posed Bayesian Inverse Problems with Infinitely Divisible and Heavy-Tailed Prior Measures
• Computational Methods for Inverse Problems
• Minorization Conditions and Convergence Rates for Markov Chain Monte Carlo
• Weak Convergence of Measures
• On the local Lipschitz stability of Bayesian inverse problems
• Two Metropolis--Hastings Algorithms for Posterior Measures with Non-Gaussian Priors in Infinite Dimensions
• Well-Posed Bayesian Inverse Problems: Priors with Exponential Tails
• Sensitivity and convergence of uniformly ergodic Markov chains
• Optimal Transport
• MCMC methods for functions: modifying old algorithms to make them faster

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