Ancestor Sampling for Particle Gibbs

Fredrik Lindsten; Michael I. Jordan; Thomas B. Schön

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arXiv · 1210.6911

Ancestor Sampling for Particle Gibbs

Fredrik Lindsten·Michael I. Jordan·Thomas B. Schön

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Abstract

We present a novel method in the family of particle MCMC methods that we refer to as particle Gibbs with ancestor sampling (PG-AS). Similarly to the existing PG with backward simulation (PG-BS) procedure, we use backward sampling to (considerably) improve the mixing of the PG kernel. Instead of using separate forward and backward sweeps as in PG-BS, however, we achieve the same effect in a single forward sweep. We apply the PG-AS framework to the challenging class of non-Markovian state-space models. We develop a truncation strategy of these models that is applicable in principle to any backward-simulation-based method, but which is particularly well suited to the PG-AS framework. In particular, as we show in a simulation study, PG-AS can yield an order-of-magnitude improved accuracy relative to PG-BS due to its robustness to the truncation error. Several application examples are discussed, including Rao-Blackwellized particle smoothing and inference in degenerate state-space models.

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Fredrik Lindsten, Michael I. Jordan, Thomas B. Schön. 2012-10-25. Ancestor Sampling for Particle Gibbs. https://arxiv.org/abs/1210.6911

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