Adaptive independence samplers

Keith, J. M., Kroese, D. P. and Sofronov, G. Y. (2008) Adaptive independence samplers. Statistics and Computing, 18 4: 409-420. doi:10.1007/s11222-008-9070-2


Author Keith, J. M.
Kroese, D. P.
Sofronov, G. Y.
Title Adaptive independence samplers
Journal name Statistics and Computing   Check publisher's open access policy
ISSN 0960-3174
Publication date 2008
Sub-type Article (original research)
DOI 10.1007/s11222-008-9070-2
Volume 18
Issue 4
Start page 409
End page 420
Total pages 12
Editor Oldford, R. W.
Place of publication United States
Publisher Springer
Collection year 2009
Language eng
Subject C1
970101 Expanding Knowledge in the Mathematical Sciences
010405 Statistical Theory
010406 Stochastic Analysis and Modelling
Abstract Markov chain Monte Carlo (MCMC) is an important computational technique for generating samples from non-standard probability distributions. A major challenge in the design of practical MCMC samplers is to achieve efficient convergence and mixing properties. One way to accelerate convergence and mixing is to adapt the proposal distribution in light of previously sampled points, thus increasing the probability of acceptance. In this paper, we propose two new adaptive MCMC algorithms based on the Independent Metropolis–Hastings algorithm. In the first, we adjust the proposal to minimize an estimate of the cross-entropy between the target and proposal distributions, using the experience of pre-runs. This approach provides a general technique for deriving natural adaptive formulae. The second approach uses multiple parallel chains, and involves updating chains individually, then updating a proposal density by fitting a Bayesian model to the population. An important feature of this approach is that adapting the proposal does not change the limiting distributions of the chains. Consequently, the adaptive phase of the sampler can be continued indefinitely. We include results of numerical experiments indicating that the new algorithms compete well with traditional Metropolis–Hastings algorithms. We also demonstrate the method for a realistic problem arising in Comparative Genomics.
Keyword Markov chain Monte Carlo
Generalized Markov sampler
Adaptive methods
Cross-entropy
Comparative genomics
Q-Index Code C1
Q-Index Status Confirmed Code

Document type: Journal Article
Sub-type: Article (original research)
Collections: 2009 Higher Education Research Data Collection
School of Mathematics and Physics
 
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Created: Wed, 18 Feb 2009, 15:00:00 EST by Marie Grove on behalf of School of Mathematics & Physics