Tran , Minh-Ngoc, Pitt, Michael K. and Kohn, Robert V. (2016) Adaptive metropolis-Hastings sampling using reversible dependent mixture proposals. Statistics and Computing, 26 . pp. 361-381. doi:10.1007/s11222-014-9509-6 ISSN 0960-3174.

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Abstract

This article develops a general-purpose adaptive sampler for sampling from a high-dimensional and/or multimodal target. The adaptive sampler is based on reversible proposal densities each of which has a mixture of multivariate t densities as its invariant density. The reversible proposals are a combination of independent and correlated components that allow the sampler to traverse the sample space efficiently as well as allowing the sampler to keep moving and exploring the sample space locally. We employ a two-chain approach, using a trial chain to adapt the proposal in the main chain. Convergence of the main chain and a strong law of large numbers are obtained under checkable conditions, and without imposing a diminishing adaptation condition. The mixtures of multivariate t densities are fitted by an efficient variational approximation algorithm in which the number of components is determined automatically. The performance of the sampler is evaluated using simulated and real examples. Our framework is quite general and can handle reversible proposal densities whose invariant densities are mixtures other than t mixtures.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Social Sciences > Economics
Library of Congress Subject Headings (LCSH):	Ergodic theory, Convergence, Multivariate analysis, Simulated annealing (Mathematics)
Journal or Publication Title:	Statistics and Computing
Publisher:	Springer
ISSN:	0960-3174
Official Date:	January 2016
Dates:	Date Event January 2016 Published 18 September 2014 Available 23 August 2013 Accepted 28 August 2013 Submitted
Volume:	26
Page Range:	pp. 361-381
DOI:	10.1007/s11222-014-9509-6
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Date of first compliant deposit:	27 January 2016
Date of first compliant Open Access:	27 January 2016
Funder:	Australian Research Council (ARC)
Grant number:	DP0667069 (ARC)

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