Error analysis in Bayesian identification of non-linear state-space models

TL;DR

This paper introduces a systematic approach using the posterior Cramér-Rao lower bound to analyze the accuracy and efficiency of Bayesian methods for identifying non-linear state-space models, highlighting their bias and MSE.

Contribution

It proposes a novel use of PCRLB for error analysis in Bayesian identification, providing a systematic way to evaluate bias, MSE, and efficiency of the estimates.

Findings

PCRLB effectively bounds the MSE of Bayesian estimates.

The approach helps identify bias and inefficiencies in existing methods.

Numerical example demonstrates the practical utility of the analysis.

Abstract

In the last two decades, several methods based on sequential Monte Carlo (SMC) and Markov chain Monte Carlo (MCMC) have been proposed for Bayesian identification of stochastic non-linear state-space models (SSMs). It is well known that the performance of these simulation based identification methods depends on the numerical approximations used in their design. We propose the use of posterior Cram\'er-Rao lower bound (PCRLB) as a mean square error (MSE) bound. Using PCRLB, a systematic procedure is developed to analyse the estimates delivered by Bayesian identification methods in terms of bias, MSE, and efficiency. The efficacy and utility of the proposed approach is illustrated through a numerical example.