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Abstract:
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Gibbs-type samplers update each of several quantities by sequentially sampling their conditional distributions under a target joint distribution. Unfortunately, this strategy can be notoriously slow to converge if the component quantities are highly correlated. We discuss a general strategy to construct more efficient samplers by replacing some of the conditional distributions with conditionals of a surrogate distribution. The surrogate is designed to share certain marginal distributions with the target, but with lower correlations among its components. Although not necessarily recognized when they were introduced a number of strategies for improving Gibbs can be formulated in this way (e.g., partially collapsed Gibbs, marginal data augmentation, ASIS interweaving, etc). In this talk, we explore the use of surrogate distributions in Gibbs-type samplers and illustrate how they may lead to incompatible updating distributions and hence sensitivity to the order of the conditional draws. Using several numerical examples, we demonstrate how different strategies involving surrogate distributions can be combined in a single sampler that outperforms any of the individual implementations.
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