Interacting Markov chain Monte Carlo methods for solving nonlinear measure-valued equations

DOI10.1214/09-AAP628zbMath1198.65024arXiv1009.5749OpenAlexW2034598556MaRDI QIDQ968777

Arnaud Doucet, Pierre Del Moral

Publication date: 6 May 2010

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

Full work available at URL: https://arxiv.org/abs/1009.5749

zbMATH Keywords

Metropolis-Hastings algorithmMarkov chain Monte Carlo methodssequential Monte Carlo methodsself-interacting processestime-inhomogeneous Markov chainsFeynman-Kac formulae

Mathematics Subject Classification ID

Computational methods in Markov chains (60J22) Nonparametric statistical resampling methods (62G09) Monte Carlo methods (65C05) Semigroups of nonlinear operators (47H20) Iterative procedures involving nonlinear operators (47J25) Signal detection and filtering (aspects of stochastic processes) (60G35) Applications of branching processes (60J85) Numerical analysis or methods applied to Markov chains (65C40) Random operators and equations (aspects of stochastic analysis) (60H25) Stochastic approximation (62L20) Integral operators (47G10) Schrödinger and Feynman-Kac semigroups (47D08)

Related Items (6)

A new class of interacting Markov chain Monte Carlo methods ⋮ Sequentially interacting Markov chain Monte Carlo methods ⋮ Fluctuations of interacting Markov chain Monte Carlo methods ⋮ A central limit theorem for adaptive and interacting Markov chains ⋮ A cautionary tale on the efficiency of some adaptive Monte Carlo schemes ⋮ Limit theorems for sequential MCMC methods

Cites Work

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• Fluctuations of interacting Markov chain Monte Carlo methods
• Equi-energy sampler with applications in statistical inference and statistical mechanics
• Sequentially interacting Markov chain Monte Carlo methods
• A functional central limit theorem for a class of interacting Markov chain Monte Carlo methods
• Rates of convergence of the Hastings and Metropolis algorithms
• Sequential Monte Carlo Methods in Practice
• On convergence of chains with occupational self–interactions
• Non-linear Markov Chain Monte Carlo
• Self-Interacting Markov Chains

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