Rigat, Fabio and Mira, Antonietta (2009) Parallel hierarchical sampling : a general-purpose class of multiple-chains MCMC algorithms. Working Paper. Coventry: University of Warwick. Centre for Research in Statistical Methodology. Working papers, Vol.2009 (No.37).

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Abstract

This paper introduces the Parallel Hierarchical Sampler (PHS), a
class of Markov chain Monte Carlo algorithms using several interacting
chains having the same target distribution but different mixing
properties. Unlike any single-chain MCMC algorithm, upon reaching
stationarity one of the PHS chains, which we call the "mother" chain,
attains exact Monte Carlo sampling of the target distribution of interest.
We empirically show that this translates in a dramatic improvement
in the sampler's performance with respect to single-chain MCMC
algorithms. Convergence of the PHS joint transition kernel is proved
and its relationships with single-chain samplers, Parallel Tempering
(PT) and variable augmentation algorithms are discussed. We then
provide two illustrative examples comparing the accuracy of PHS with that of various Metropolis-Hastings and PT for sampling multimodal
mixtures of multivariate Gaussian densities and for 'banana-shaped'
multivariate distributions with heavy tails. Finally, PHS is applied
to approximate inferences for two Bayesian model uncertainty problems,
namely selection of main effects for a linear Gaussian multiple
regression model and inference for the structure of an exponential treed
survival model.

Item Type:	Working or Discussion Paper (Working Paper)
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH):	Markov processes, Monte Carlo method, Sampling (Statistics)
Series Name:	Working papers
Publisher:	University of Warwick. Centre for Research in Statistical Methodology
Place of Publication:	Coventry
Official Date:	2009
Dates:	Date Event 2009 Published
Volume:	Vol.2009
Number:	No.37
Number of Pages:	55
Status:	Not Peer Reviewed
Access rights to Published version:	Open Access
Funder:	University of Insubria, Italy. Ministero dell'istruzione, dell'università e della ricerca (MIUR)
Grant number:	2007XECZ7L 003 (MIUR)

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