On Particle Methods for Parameter Estimation in State-Space Models

TL;DR

This paper reviews particle methods, specifically Sequential Monte Carlo techniques, for estimating static parameters in nonlinear, non-Gaussian state-space models, highlighting their advantages, limitations, and performance in various applications.

Contribution

It provides a comprehensive overview of advanced particle methods for static parameter estimation in complex state-space models, including their comparative analysis.

Findings

Particle methods effectively estimate static parameters in nonlinear models.

Limitations include computational complexity and potential degeneracy issues.

Performance varies depending on model complexity and data quality.

Abstract

Nonlinear non-Gaussian state-space models are ubiquitous in statistics, econometrics, information engineering and signal processing. Particle methods, also known as Sequential Monte Carlo (SMC) methods, provide reliable numerical approximations to the associated state inference problems. However, in most applications, the state-space model of interest also depends on unknown static parameters that need to be estimated from the data. In this context, standard particle methods fail and it is necessary to rely on more sophisticated algorithms. The aim of this paper is to present a comprehensive review of particle methods that have been proposed to perform static parameter estimation in state-space models. We discuss the advantages and limitations of these methods and illustrate their performance on simple models.