Mixing of MCMC algorithms

We analyse MCMC chains focusing on how to find simulation parameters that give good mixing for discrete time, Harris ergodic Markov chains on a general state space X having invariant distribution π. The analysis uses an upper bound for the variance of the probability estimate. For each simulation pa...

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Bibliographic Details
Published inJournal of statistical computation and simulation Vol. 89; no. 12; pp. 2261 - 2279
Main Author Holden, Lars
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 13.08.2019
Taylor & Francis Ltd
Subjects
Acceptance rates in Metropolis-Hastings algorithm
Algorithms
Computer simulation
Intervals
Markov analysis
Markov chains
MCMC
mixing
optimal step length
Parameter estimation
recurrence
Simulation
Upper bounds
variance estimates
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Summary:We analyse MCMC chains focusing on how to find simulation parameters that give good mixing for discrete time, Harris ergodic Markov chains on a general state space X having invariant distribution π. The analysis uses an upper bound for the variance of the probability estimate. For each simulation parameter set, the bound is estimated from an MCMC chain using recurrence intervals. Recurrence intervals are a generalization of recurrence periods for discrete Markov chains. It is easy to compare the mixing properties for different simulation parameters. The paper gives general advice on how to improve the mixing of the MCMC chains and a new methodology for how to find an optimal acceptance rate for the Metropolis-Hastings algorithm. Several examples, both toy examples and large complex ones, illustrate how to apply the methodology in practice. We find that the optimal acceptance rate is smaller than the general recommendation in the literature in some of these examples.
ISSN:0094-9655
1563-5163
DOI:10.1080/00949655.2019.1615064