Parallel Multivariate Slice Sampling

Open Access
- Author:
- Tibbits, Matthew McLean
- Graduate Program:
- Statistics
- Degree:
- Master of Science
- Document Type:
- Master Thesis
- Date of Defense:
- None
- Committee Members:
- Murali Haran, Thesis Advisor/Co-Advisor
John C Liechty, Thesis Advisor/Co-Advisor - Keywords:
- Bayesian inference; Markov chain Monte Carlo; Para
- 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 each evaluation is 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, often resulting 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 architecture, 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.