Couplings of Particle Filters

Particle filters provide Monte Carlo approximations of intractable quantities, such as likelihood evaluations in state-space models. In many cases, the interest does not lie in the values of the estimates themselves, but in the comparison of these values for various parameters. For instance, we might want to compare the likelihood at two parameter values. Such a comparison is facilitated by introducing positive correlations between the estimators, which is a standard variance reduction technique. In the context of particle filters, this calls for new resampling schemes. We propose coupled resampling schemes, and show how they improve the performance of finite difference estimators and pseudo-marginal algorithms for parameter inference. Furthermore, coupled resampling schemes can be embedded into debiasing algorithms (Rhee & Glynn 2014), leading to a new smoothing algorithm which is easy to parallelize and, for the first time, produces error estimators for smoothing quantities.