Diagnostics for insufficiencies of posterior calculations in Bayesian signal inference

TL;DR

This paper introduces a diagnostic method to identify and differentiate various errors in posterior distributions within Bayesian signal inference, enhancing validation of inference accuracy.

Contribution

It extends previous work by providing a way to detect and distinguish multiple types of errors in posterior calculations, including in multidimensional cases.

Findings

The method reveals deviations from the correct posterior.

It discriminates between different numerical and approximation errors.

Applicable to multidimensional signals.

Abstract

We present an error-diagnostic validation method for posterior distributions in Bayesian signal inference, an advancement of a previous work. It transfers deviations from the correct posterior into characteristic deviations from a uniform distribution of a quantity constructed for this purpose. We show that this method is able to reveal and discriminate several kinds of numerical and approximation errors, as well as their impact on the posterior distribution. For this we present four typical analytical examples of posteriors with incorrect variance, skewness, position of the maximum, or normalization. We show further how this test can be applied to multidimensional signals.