Forward Smoothing using Sequential Monte Carlo

TL;DR

This paper introduces a forward smoothing SMC algorithm that improves variance behavior over time, enabling efficient online parameter estimation in non-linear state-space models.

Contribution

It presents a novel forward-only SMC algorithm that reduces variance growth and facilitates online maximum likelihood estimation, addressing particle degeneracy issues.

Findings

Asymptotic variance increases linearly with time

Enables online maximum likelihood parameter estimation

Reduces particle path degeneracy

Abstract

Sequential Monte Carlo (SMC) methods are a widely used set of computational tools for inference in non-linear non-Gaussian state-space models. We propose a new SMC algorithm to compute the expectation of additive functionals recursively. Essentially, it is an online or forward-only implementation of a forward filtering backward smoothing SMC algorithm proposed in Doucet .et .al (2000). Compared to the standard path space SMC estimator whose asymptotic variance increases quadratically with time even under favourable mixing assumptions, the asymptotic variance of the proposed SMC estimator only increases linearly with time. This forward smoothing procedure allows us to implement on-line maximum likelihood parameter estimation algorithms which do not suffer from the particle path degeneracy problem.