Parameter Estimation via Conditional Expectation --- A Bayesian Inversion

TL;DR

This paper discusses a Bayesian approach to parameter estimation in models using conditional expectation, highlighting its theoretical foundation and numerical implementation for identifying uncertain parameters from observed data.

Contribution

It introduces a Bayesian inversion method based on conditional expectation and explores numerical approximation techniques for practical computation.

Findings

Theoretical framework for Bayesian parameter estimation using conditional expectation.

Numerical methods for approximating conditional expectations in practice.

Application potential for system identification and uncertainty quantification.

Abstract

When a mathematical or computational model is used to analyse some system, it is usual that some parameters resp.\ functions or fields in the model are not known, and hence uncertain. These parametric quantities are then identified by actual observations of the response of the real system. In a probabilistic setting, Bayes's theory is the proper mathematical background for this identification process. The possibility of being able to compute a conditional expectation turns out to be crucial for this purpose. We show how this theoretical background can be used in an actual numerical procedure, and shortly discuss various numerical approximations.