Ancestor Sampling for Particle Gibbs

TL;DR

This paper introduces particle Gibbs with ancestor sampling (PG-AS), a novel method that improves mixing and accuracy in particle MCMC, especially for non-Markovian models, by integrating backward sampling into a single forward sweep.

Contribution

The paper proposes PG-AS, a new particle MCMC method that combines backward sampling with a single forward sweep, enhancing efficiency and robustness in non-Markovian state-space models.

Findings

PG-AS significantly improves accuracy over PG-BS.

PG-AS demonstrates robustness to truncation errors.

Applications include Rao-Blackwellized smoothing and degenerate models.

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.