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Abstract:
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Slice sampling provides a nearly automatic 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. (ii) Since it is challenging to construct multivariate updates, the updates are typically univariate, often resulting in slow mixing samplers. We propose a grid-based 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 60,000 threads simultaneously. We demonstrate that it is possible to construct a multivariate slice sampler that is both fast mixing and efficient in terms of computing time.
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