Parallel hierarchical sampling : a general-purpose class of multiple-chains MCMC algorithms
Rigat, Fabio, 1975- 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).
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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|
|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|Status:||Not Peer Reviewed|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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