Parallel multivariate slice sampling

Matthew M. Tibbits, Murali Haran, John C. Liechty

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

Slice sampling provides an easily implemented method for constructing a Markov chain Monte Carlo (MCMC) algorithm. However, slice sampling has two major drawbacks: (i) it requires repeated evaluation of likelihoods for each update, which can make it impractical when evaluations are expensive or as the number of evaluations grows (geometrically) with the dimension of the slice sampler, and (ii) since it can be challenging to construct multivariate updates, the updates are typically univariate, which often results in slow mixing samplers. We propose an approach to multivariate slice sampling that naturally lends itself to a parallel implementation. Our approach takes advantage of recent advances in computer architectures, for instance, the newest generation of graphics cards can execute roughly 30,000 threads simultaneously. We demonstrate that it is possible to construct a multivariate slice sampler that has good mixing properties and is efficient in terms of computing time. The contributions of this article are therefore twofold. We study approaches for constructing a multivariate slice sampler, and we show how parallel computing can be useful for making MCMC algorithms computationally efficient. We study various implementations of our algorithm in the context of real and simulated data.

Original languageEnglish (US)
Pages (from-to)415-430
Number of pages16
JournalStatistics and Computing
Volume21
Issue number3
DOIs
StatePublished - Jul 1 2011

Fingerprint

Slice
Sampling
Markov processes
Computer architecture
Markov Chain Monte Carlo Algorithms
Update
Parallel processing systems
Evaluation
Computer Architecture
Parallel Computing
Parallel Implementation
Thread
Univariate
Likelihood
Computing
Demonstrate
Markov chain Monte Carlo

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Computational Theory and Mathematics

Cite this

Tibbits, Matthew M. ; Haran, Murali ; Liechty, John C. / Parallel multivariate slice sampling. In: Statistics and Computing. 2011 ; Vol. 21, No. 3. pp. 415-430.
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Parallel multivariate slice sampling. / Tibbits, Matthew M.; Haran, Murali; Liechty, John C.

In: Statistics and Computing, Vol. 21, No. 3, 01.07.2011, p. 415-430.

Research output: Contribution to journalArticle

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