Minimising MCMC variance via diffusion limits, with an application to simulated tempering

DOI10.1214/12-AAP918zbMath1298.60078arXiv1401.3559MaRDI QIDQ2443188

Jeffrey S. Rosenthal, Gareth O. Roberts

Publication date: 4 April 2014

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

Full work available at URL: https://arxiv.org/abs/1401.3559

zbMATH Keywords

Markov chain Monte Carlooptimal scalingdiffusion limitssimulated tempering

Mathematics Subject Classification ID

Computational methods in Markov chains (60J22) Point estimation (62F10) Markov processes: estimation; hidden Markov models (62M05) Numerical analysis or methods applied to Markov chains (65C40)

Related Items

Asymptotic analysis of the random walk metropolis algorithm on ridged densities, Jump Markov chains and rejection-free Metropolis algorithms, Unnamed Item, Spectral gap of replica exchange Langevin diffusion on mixture distributions, Constructing optimal transition matrix for Markov chain Monte Carlo, Optimal scaling of random-walk Metropolis algorithms on general target distributions, Variational principles for asymptotic variance of general Markov processes, Optimal scaling of the random walk Metropolis algorithm under L^p mean differentiability, State-dependent swap strategies and automatic reduction of number of temperatures in adaptive parallel tempering algorithm, Accelerating parallel tempering: Quantile tempering algorithm (QuanTA), Bayesian computation: a summary of the current state, and samples backwards and forwards, Weight-preserving simulated tempering, Peskun-Tierney ordering for Markovian Monte Carlo: beyond the reversible scenario, Efficiency of delayed-acceptance random walk metropolis algorithms, The simulated tempering method in the infinite switch limit with adaptive weight learning, On the efficiency of pseudo-marginal random walk Metropolis algorithms, Skew brownian motion and complexity of the alps algorithm

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Convergence of adaptive and interacting Markov chain Monte Carlo algorithms
• Towards optimal scaling of Metropolis-coupled Markov chain Monte Carlo
• A note on Metropolis-Hastings kernels for general state spaces
• Weak convergence and optimal scaling of random walk Metropolis algorithms
• Ordering and improving the performance of Monte Carlo Markov chains.
• Optimal scaling for various Metropolis-Hastings algorithms.
• A diffusion approximation for a Markovian queue with reneging
• Markov chains for exploring posterior distributions. (With discussion)
• Optimal scalings for local Metropolis-Hastings chains on nonproduct targets in high dimensions
• Weak convergence of Metropolis algorithms for non-I.I.D. target distributions
• Optimal acceptance rates for Metropolis algorithms: Moving beyond 0.234
• Optimum Monte-Carlo sampling using Markov chains
• Handbook of Markov Chain Monte Carlo
• Optimal scaling of Metropolis algorithms: Heading toward general target distributions
• Optimal Scaling of Discrete Approximations to Langevin Diffusions
• Improved Bounds for Mixing Rates of Markov Chains and Multicommodity Flow
• Covariance structure of the Gibbs sampler with applications to the comparisons of estimators and augmentation schemes