Rejection-Sampling-Based Ancestor Sampling for Particle Gibbs

Particle Gibbs with ancestor sampling is an efficient and statistically principled algorithm for learning of dynamic systems. However, the ancestor sampling step used to improve mixing of the Markov chain requires the possibly expensive calculation of a set of ancestor weights for the complete particle system. In this paper, we propose a rejection-sampling-based algorithm for ancestor sampling in particle Gibbs that mitigates this problem. Additionally, performance guarantees and a fallback strategy to prevent suffering from high rejection rates are discussed. The performance of the method is illustrated in two numerical examples.