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Searching for efficient Markov chain Monte Carlo proposal kernels

Yang, Z; Rodríguez, CE; (2013) Searching for efficient Markov chain Monte Carlo proposal kernels. Proceedings of the National Academy of Sciences , 110 (48) pp. 19307-19312. 10.1073/pnas.1311790110. Green open access

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Abstract

Markov chain Monte Carlo (MCMC) or the Metropolis-Hastings algorithm is a simulation algorithm that has made modern Bayesian statistical inference possible. Nevertheless, the efficiency of different Metropolis-Hastings proposal kernels has rarely been studied except for the Gaussian proposal. Here we propose a unique class of Bactrian kernels, which avoid proposing values that are very close to the current value, and compare their efficiency with a number of proposals for simulating different target distributions, with efficiency measured by the asymptotic variance of a parameter estimate. The uniform kernel is found to be more efficient than the Gaussian kernel, whereas the Bactrian kernel is even better. When optimal scales are used for both, the Bactrian kernel is at least 50% more efficient than the Gaussian. Implementation in a Bayesian program for molecular clock dating confirms the general applicability of our results to generic MCMC algorithms. Our results refute a previous claim that all proposals had nearly identical performance and will prompt further research into efficient MCMC proposals.

Type: Article
Title: Searching for efficient Markov chain Monte Carlo proposal kernels
Location: United States
Open access status: An open access version is available from UCL Discovery
DOI: 10.1073/pnas.1311790110
Publisher version: http://dx.doi.org/10.1073/pnas.1311790110
Language: English
Additional information: Copyright © The Authors 2013.
Keywords: Bayesian inference, convergence rate, mixing, Algorithms, Bayes Theorem, Computer Simulation, Markov Chains, Monte Carlo Method
UCL classification: UCL
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Life Sciences
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Life Sciences > Div of Biosciences
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Life Sciences > Div of Biosciences > Genetics, Evolution and Environment
URI: https://discovery.ucl.ac.uk/id/eprint/1473661
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