Where Bayes tweaks Gauss: Conditionally Gaussian priors for stable multi-dipole estimation

TL;DR

This paper introduces a simple generalization of a dipole estimation model using a log-uniform hyperprior, which enhances stability and reduces hyperparameter dependence in magneto/electro-encephalographic data analysis.

Contribution

It proposes a novel hyperprior for the model's parameters, improving robustness and stability in multi-dipole estimation tasks.

Findings

Posterior approximation remains stable across hyperparameter values

Reduces dependence on hyperparameter in dipole estimation

Demonstrated effectiveness with simulations and real data

Abstract

We present a very simple yet powerful generalization of a previously described model and algorithm for estimation of multiple dipoles from magneto/electro-encephalographic data. Specifically, the generalization consists in the introduction of a log-uniform hyperprior on the standard deviation of a set of conditionally linear/Gaussian variables. We use numerical simulations and an experimental dataset to show that the approximation to the posterior distribution remains extremely stable under a wide range of values of the hyperparameter, virtually removing the dependence on the hyperparameter.