On the Role of Decision Theory in Uncertainty Analysis

TL;DR

This paper compares MLE and HPE in industrial uncertainty analysis through decision theory, highlighting the advantages of Bayesian estimators with carefully chosen cost functions for better uncertainty quantification.

Contribution

It demonstrates that HPE is equivalent to Bayes estimation under certain conditions and advocates for systematic use of Bayes estimators with explicit cost functions.

Findings

MLE may inadequately account for uncertainty with limited data

HPE aligns with Bayes estimation for specific cost functions

Bayesian estimators should be systematically used with well-defined costs

Abstract

Maximum likelihood estimation (MLE) and heuristic predictive estimation (HPE) are two widely used approaches in industrial uncertainty analysis. We review them from the point of view of decision theory, using Bayesian inference as a gold standard for comparison. The main drawback of MLE is that it may fail to properly account for the uncertainty on the physical process generating the data, especially when only a small amount of data are available. HPE offers an improvement in that it takes this uncertainty into account. However, we show that this approach is actually equivalent to Bayes estimation for a particular cost function that is not explicitly chosen by the decision maker. This may produce results that are suboptimal from a decisional perspective. These results plead for a systematic use of Bayes estimators based on carefully defined cost functions.