Robust particle filters via sequential pairwise reparameterized Gibbs sampling

Sequential Monte Carlo (“particle filtering”) methods provide a powerful set of tools for recursive optimal Bayesian filtering in state-space models. However, these methods are based on importance sampling, which is known to be non-robust in several key scenarios, and therefore standard particle filtering methods can fail in these settings. We present a filtering method which solves the key forward recursion using a reparameterized Gibbs sampling method, thus sidestepping the need for importance sampling. In many cases the resulting filter is much more robust and efficient than standard importance-sampling particle filter implementations. We illustrate the method with an application to a nonlinear, non-Gaussian model from neuroscience.