On the Forward Filtering Backward Smoothing particle approximations of the smoothing distribution in general state spaces models

Abstract

A prevalent problem in general state-space models is the approximation of the smoothing distribution of a state, or a sequence of states, conditional on the observations from the past, the present, and the future. The aim of this paper is to provide a rigorous foundation for the calculation, or approximation, of such smoothed distributions, and to analyse in a common unifying framework different schemes to reach this goal. Through a cohesive and generic exposition of the scientific literature we offer several novel extensions allowing to approximate joint smoothing distribution in the most general case with a cost growing linearly with the number of particles.

References in corpus (1)

• Central limit theorem for sequential Monte Carlo methods and its application to Bayesian inference

Cited by in corpus (5)

• Lookahead Strategies for Sequential Monte Carlo
• Approximate Smoothing and Parameter Estimation in High-Dimensional State-Space Models
• Scaling Multidimensional Inference for Structured Gaussian Processes
• A Backward Particle Interpretation of Feynman-Kac Formulae
• Marginal Likelihood Computation for Hidden Markov Models via Generalized Two-Filter Smoothing