Particle Gibbs with refreshed backward simulation

The particle Gibbs algorithm can be used for Bayesian parameter estimation in Markovian state space models. Sometimes the resulting Markov chains mix slowly when the component particle filter suffers from degeneracy. This effect can be somewhat alleviated using backward simulation. In this paper we show how a simple modification to this scheme, which we refer to as refreshed backward simulation, can further improve the mixing. This works by sampling new state values simultaneously with the corresponding ancestor indexes. Although the necessary conditional distributions cannot be sampled directly, we provide suitable Markov kernels which target them. The efficacy of this new scheme is demonstrated with a simulation example.