Replica Conditional Sequential Monte Carlo

TL;DR

This paper introduces a replica conditional SMC method that leverages information from multiple replicas to improve state inference in non-linear non-Gaussian models, demonstrating superior empirical performance over standard methods.

Contribution

The paper proposes a novel replica cSMC scheme that uses multiple replicas to incorporate full observation sequences, enhancing inference accuracy and parallelizability.

Findings

Outperforms standard iterated cSMC at fixed computational cost

Easily parallelizable implementation

Shows excellent empirical results in complex models

Abstract

We propose a Markov chain Monte Carlo (MCMC) scheme to perform state inference in non-linear non-Gaussian state-space models. Current state-of-the-art methods to address this problem rely on particle MCMC techniques and its variants, such as the iterated conditional Sequential Monte Carlo (cSMC) scheme, which uses a Sequential Monte Carlo (SMC) type proposal within MCMC. A deficiency of standard SMC proposals is that they only use observations up to time $t$ to propose states at time $t$ when an entire observation sequence is available. More sophisticated SMC based on lookahead techniques could be used but they can be difficult to put in practice. We propose here replica cSMC where we build SMC proposals for one replica using information from the entire observation sequence by conditioning on the states of the other replicas. This approach is easily parallelizable and we demonstrate its excellent empirical performance when compared to the standard iterated cSMC scheme at fixed computational complexity.