A Note on Particle Gibbs Method and its Extensions and Variants

High-dimensional state trajectories of state-space models pose challenges for Bayesian inference. Particle Gibbs (PG) methods have been widely used to sample from the posterior of a state space model. Basically, particle Gibbs is a Particle Markov Chain Monte Carlo (PMCMC) algorithm that mimics the Gibbs sampler by drawing model parameters and states from their conditional distributions. This tutorial provides an introductory view on Particle Gibbs (PG) method and its extensions and variants, and illustrates through several examples of inference in non-linear state space models (SSMs). We also implement PG Samplers in two different programming languages: Python and Rust. Comparison of run-time performance of Python and Rust programs are also provided for various PG methods.