Efficient strategy for the Markov chain Monte Carlo in high-dimension with heavy-tailed target probability distribution

DOI10.3150/17-BEJ976zbMath1407.60102arXiv1412.6231MaRDI QIDQ1750100

Kengo Kamatani

Publication date: 18 May 2018

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1412.6231

zbMATH Keywords

consistencyMonte CarloMalliavin calculusStein's methodMarkov chain

Mathematics Subject Classification ID

Computational methods in Markov chains (60J22) Monte Carlo methods (65C05) Stochastic calculus of variations and the Malliavin calculus (60H07) Convergence of probability measures (60B10)

Related Items (11)

Hybrid estimators for stochastic differential equations from reduced data ⋮ Non-reversible guided Metropolis kernel ⋮ Adaptation of the tuning parameter in general Bayesian inference with robust divergence ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Hybrid estimation for ergodic diffusion processes based on noisy discrete observations ⋮ Hybrid estimators for small diffusion processes based on reduced data ⋮ Random walk Metropolis algorithm in high dimension with non-Gaussian target distributions ⋮ Quasi-likelihood analysis and Bayes-type estimators of an ergodic diffusion plus noise ⋮ Estimation of risk contributions with MCMC ⋮ High-dimensional scaling limits of piecewise deterministic sampling algorithms

Uses Software

• CODA

Cites Work

• Spectral gaps for a Metropolis-Hastings algorithm in infinite dimensions
• Stein's method on Wiener chaos
• Derivatives of Wiener functionals and absolute continuity of induced measures
• Weak convergence and optimal scaling of random walk Metropolis algorithms
• Markov chains for exploring posterior distributions. (With discussion)
• Hybrid multi-step estimators for stochastic differential equations based on sampled data
• Optimal scalings for local Metropolis-Hastings chains on nonproduct targets in high dimensions
• Local consistency of Markov chain Monte Carlo methods
• Error bounds for Metropolis-Hastings algorithms applied to perturbations of Gaussian measures in high dimensions
• Normal Approximations with Malliavin Calculus
• The Malliavin Calculus and Related Topics
• Normal Approximation by Stein’s Method
• Optimal Scaling of Discrete Approximations to Langevin Diffusions
• Ergodicity of Markov chain Monte Carlo with reversible proposal
• Multivariate T-Distributions and Their Applications
• MCMC methods for functions: modifying old algorithms to make them faster
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