Approximating Posterior Predictive Distributions by Averaging Output From Many Particle Filters

TL;DR

This paper presents a parallel algorithm called particle swarm filter that approximates posterior predictive distributions by averaging multiple particle filters, supported by theoretical guarantees and numerical experiments.

Contribution

The paper introduces the particle swarm filter, a novel parallel method for approximating posterior predictive distributions using multiple particle filters.

Findings

Law of large numbers and central limit theorem established for the method.

Numerical study demonstrates effectiveness on stochastic volatility model.

Algorithm is recursive and embarrassingly parallel.

Abstract

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.