Generation path-switching in sequential Monte-Carlo methods

Abstract

Traditional sequential Monte-Carlo methods suffer from weight degeneracy which is where the number of distinct particles collapse. This is a particularly debilitating problem in many practical applications. A new method, the adaptive path particle filter, based on the generation gap concept from evolutionary computation, is proposed for recursive Bayesian estimation of non-linear non-Gaussian dynamical systems. A generation-based path evaluation step is embedded into the general sequential importance resampling algorithm leveraging the descriptive ability of discarded particles. A simulation example of the stochastic volatility problem is presented. In this simulation, the adaptive path particle filter is greatly superior to the standard particle filter and the Markov chain Monte-Carlo particle filter. We present a detailed analysis of the results, and suggest directions for future research.

State Space Modeling & Bayesian Inference with Computational Intelligence

“…in which we represent the observation vector at time t by y t 2 R p , which satis¯es (1) where h t : R n  R r ! R p is the observation function and v t 2 R r is the state error term whose known distribution is independent of both system noise and time.…”