Classical vs. Bayesian methods for linear system identification: point estimators and confidence sets

TL;DR

This paper compares classical and Bayesian approaches for linear system identification, focusing on point estimators and confidence sets, highlighting differences in their performance and applicability.

Contribution

It introduces a comprehensive comparison between classical and Bayesian methods, including a Full Bayes solution and Empirical Bayes approximation, for system identification.

Findings

Bayesian methods provide different confidence regions compared to classical methods.

Full Bayes approach offers a comprehensive probabilistic framework.

Empirical Bayes approximation balances computational efficiency with accuracy.

Abstract

This paper compares classical parametric methods with recently developed Bayesian methods for system identification. A Full Bayes solution is considered together with one of the standard approximations based on the Empirical Bayes paradigm. Results regarding point estimators for the impulse response as well as for confidence regions are reported.