Convergence rates for residual branching particle filters

A large class of proven discrete-time branching particle filters with Bayesian model selection capabilities and effective resampling is analyzed mathematically. The particles interact weakly in the branching procedure through the total mass process in such a way that the expected number of particles can remain constant. The weighted particle filter, which has no resampling, and the fully-resampled branching particle filter are included in the class as extreme points. Otherwise, selective residual branching is used allowing any number of offspring. Each particle filter in the class is coupled to a McKean-Vlasov particle system, corresponding to a reduced, unimplementable branching particle filter, for which Marcinkiewicz strong laws of large numbers (Mllns) and the central limit theorem (clt) can be written down. Coupling arguments are used to show the reduced system can be used to predict performance of and to transfer the Mllns to the real weakly-interacting residual branching particle filter. This clt is also shown transferable when (a few) extra particles are used.