Approximating Posterior Predictive Distributions by Averaging Output From Many Particle Filters

This paper introduces the {\it particle swarm filter} (not to be confused with particle swarm optimization): a recursive and embarrassingly parallel algorithm that targets an approximation to the sequence of posterior predictive distributions by averaging expectation approximations from many particle filters. A law of large numbers and a central limit theorem are provided, as well as an numerical study of simulated data from a stochastic volatility model.