Computation of Expectations by Markov Chain Monte Carlo Methods

DOI10.1007/978-3-319-08159-5_20zbMath1317.65017arXiv1311.1899OpenAlexW2113574707MaRDI QIDQ5256571

Erich Novak, Daniel Rudolf

Publication date: 18 June 2015

Published in: Extraction of Quantifiable Information from Complex Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1311.1899

zbMATH Keywords

surveyMarkov chain Monte Carlo methoderror boundintegralexpectationtractabilitycurse of dimension

Mathematics Subject Classification ID

Computational methods in Markov chains (60J22) Monte Carlo methods (65C05) Numerical analysis or methods applied to Markov chains (65C40) Research exposition (monographs, survey articles) pertaining to numerical analysis (65-02)

Related Items (6)

Some Results on the Complexity of Numerical Integration ⋮ Wasserstein contraction and spectral gap of slice sampling revisited ⋮ Dimension‐independent Markov chain Monte Carlo on the sphere ⋮ Dimension-independent spectral gap of polar slice sampling ⋮ Mixing and concentration by Ricci curvature ⋮ Quantitative spectral gap estimate and Wasserstein contraction of simple slice sampling

Cites Work

• Discrepancy bounds for uniformly ergodic Markov chain quasi-Monte Carlo
• Consistency of Markov chain quasi-Monte Carlo on continuous state spaces
• Curvature, concentration and error estimates for Markov chain Monte Carlo
• Tractability of multivariate problems. Volume III: Standard information for operators
• Positivity of hit-and-run and related algorithms
• Tractability of multivariate problems. Volume I: Linear information
• General state space Markov chains and MCMC algorithms
• Tractability of multivariate problems. Volume II: Standard information for functionals.
• Geometric ergodicity and hybrid Markov chains
• Rates of convergence of the Hastings and Metropolis algorithms
• Error bounds of MCMC for functions with unbounded stationary variance
• On the computational complexity of MCMC-based estimators in large samples
• Nonasymptotic bounds on the estimation error of MCMC algorithms
• Simple Monte Carlo and the Metropolis algorithm
• Explicit error bounds for Markov chain Monte Carlo
• Hit-and-Run for Numerical Integration
• Geometric L² and ^{L1 convergence are equivalent for reversible Markov chains}
• Bounds on the L 2 Spectrum for Markov Chains and Markov Processes: A Generalization of Cheeger's Inequality
• Efficient Monte Carlo Procedures for Generating Points Uniformly Distributed over Bounded Regions
• Hit-and-Run from a Corner

This page was built for publication: Computation of Expectations by Markov Chain Monte Carlo Methods