Covariant priors and model uncertainty

TL;DR

This paper explores how differential geometry can be used to develop covariant priors in Bayesian metrology, addressing paradoxes and parameterization issues to improve model uncertainty estimation.

Contribution

It provides an overview of information geometry, investigates key paradoxes, and proposes solutions to maintain covariance in Bayesian model uncertainty estimation.

Findings

Identified paradoxes in multi-parameter problems

Developed alternative methods preserving covariance

Enhanced understanding of geometric approaches in Bayesian inference

Abstract

In the application of Bayesian methods to metrology, pre-data probabilities play a critical role in the estimation of the model uncertainty. Following the observation that distributions form Riemann's manifolds, methods of differential geometry can be applied to ensure covariant priors and uncertainties independent of parameterization. Paradoxes were found in multi-parameter problems and alternatives were developed; but, when different parameters are of interest, covariance may be lost. This paper overviews information geometry, investigates some key paradoxes, and proposes solutions that preserve covariance.