The parameters uncertainty inflation fallacy

TL;DR

This paper critically reviews how current methods inflate parameter uncertainty to account for model inadequacy in physical models, revealing biases that prevent accurate prediction uncertainty estimation.

Contribution

It identifies biases in existing parameter uncertainty inflation methods and highlights the need for improved approaches to accurately reflect model inadequacy errors.

Findings

Current methods are biased and do not produce accurate uncertainty bands.

Biases hinder transferability of uncertainty estimates to other quantities.

A critical review of computational chemistry implementations is provided.

Abstract

Statistical estimation of the prediction uncertainty of physical models is typically hindered by the inadequacy of these models due to various approximations they are built upon. The prediction errors due to model inadequacy can be handled either by correcting the model's results, or by adapting the model's parameters uncertainty to generate prediction uncertainty representative, in a way to be defined, of model inadequacy errors. The main advantage of the latter approach is its transferability to the prediction of other quantities of interest based on the same parameters. A critical review of state-of-the-art implementations of this approach in computational chemistry shows that it is biased, in the sense that it does not produce prediction uncertainty bands conforming with model inadequacy errors.