Optimal scaling for partially updating MCMC algorithms

Neal, Peter John and Roberts, Gareth (2006) Optimal scaling for partially updating MCMC algorithms. Annals of Applied Probability, 16 (2). pp. 475-515. ISSN 1050-5164

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In this paper we shall consider optimal scaling problems for high-dimensional Metropolis–Hastings algorithms where updates can be chosen to be lower dimensional than the target density itself. We find that the optimal scaling rule for the Metropolis algorithm, which tunes the overall algorithm acceptance rate to be 0.234, holds for the so-called Metropolis-within-Gibbs algorithm as well. Furthermore, the optimal efficiency obtainable is independent of the dimensionality of the update rule. This has important implications for the MCMC practitioner since high-dimensional updates are generally computationally more demanding, so that lower-dimensional updates are therefore to be preferred. Similar results with rather different conclusions are given for so-called Langevin updates. In this case, it is found that high-dimensional updates are frequently most efficient, even taking into account computing costs.

Item Type:
Journal Article
Journal or Publication Title:
Annals of Applied Probability
Uncontrolled Keywords:
?? statistics and probabilitystatistics, probability and uncertainty ??
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27 Nov 2015 16:02
Last Modified:
15 Jul 2024 15:37