On the Value of derivative evaluations and random walk suppression in Markov Chain Monte Carlo algorithms |
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| Authors: | Gustafson Paul MacNab Ying C Wen Sijin |
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| Institution: | (1) Department of Statistics, University of British Columbia, Vancouver, British Columbia, Canada;(2) Centre for Health Care Innovation and Improvement, British Columbia Institute for Children's and Women's Health, Vancouver, British Columbia, Canada;;(3) Department of Health Care and Epidemiology, University of British Columbia, Vancouver, British Columbia, Canada;(4) Department of Biostatistics, University of Texas M.D. Anderson Cancer Center, Houston, Texas, USA |
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| Abstract: | Two strategies that can potentially improve Markov Chain Monte Carlo algorithms are to use derivative evaluations of the target density, and to suppress random walk behaviour in the chain. The use of one or both of these strategies has been investigated in a few specific applications, but neither is used routinely. We undertake a broader evaluation of these techniques, with a view to assessing their utility for routine use. In addition to comparing different algorithms, we also compare two different ways in which the algorithms can be applied to a multivariate target distribution. Specifically, the univariate version of an algorithm can be applied repeatedly to one-dimensional conditional distributions, or the multivariate version can be applied directly to the target distribution. |
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| Keywords: | hybrid Monte Carlo Langevin Monte Carlo Markov chain Monte Carlo Metropolis-Hastings algorithm random walk suppression |
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