Evaluating the Role of Sequential Monte Carlo Methods in Bayesian Updating and State Space Modeling

Posted: Dec 24, 2000

• Amelia Rogers
• Andrew Powell
• Anthony Parker

Abstract

Sequential Monte Carlo methods, commonly known as particle filters, have emerged as a powerful framework for Bayesian inference in state space models. These methods provide a flexible approach to sequential Bayesian updating that accommodates non-linear dynamics and non-Gaussian noise distributions. The fundamental principle underlying SMC methods involves representing the posterior distribution through a set of weighted particles that are propagated and updated sequentially as new observations become available. This approach stands in contrast to traditional filtering methods that often impose restrictive assumptions about system linearity and noise characteristics. Despite their theoretical advantages, practical implementation of SMC methods faces significant challenges related to particle degeneracy, computational complexity, and the curse of dimensionality. This paper addresses these challenges through a novel adaptive resampling framework that dynamically adjusts resampling thresholds and incorporates systematic rejuvenation procedures. Our approach represents a departure from conventional fixed-threshold resampling schemes by allowing the algorithm to adapt to the local characteristics of the posterior distribution. We demonstrate that this adaptive framework significantly improves computational efficiency while maintaining estimation accuracy across diverse application domains.