Variational Bayesian modelling of mixed-effects
This work addresses the problem of mixed-effects modeling for researchers in fields like psychology or neuroscience, but it appears incremental as it builds on existing variational Bayesian and empirical Bayes approaches.
The paper tackles the challenge of accurately and efficiently modeling mixed-effects in group studies using variational Bayesian methods, resulting in a computationally efficient scheme that can assess statistical significance and capture inter-individual differences.
This note is concerned with an accurate and computationally efficient variational bayesian treatment of mixed-effects modelling. We focus on group studies, i.e. empirical studies that report multiple measurements acquired in multiple subjects. When approached from a bayesian perspective, such mixed-effects models typically rely upon a hierarchical generative model of the data, whereby both within- and between-subject effects contribute to the overall observed variance. The ensuing VB scheme can be used to assess statistical significance at the group level and/or to capture inter-individual differences. Alternatively, it can be seen as an adaptive regularization procedure, which iteratively learns the corresponding within-subject priors from estimates of the group distribution of effects of interest (cf. so-called "empirical bayes" approaches). We outline the mathematical derivation of the ensuing VB scheme, whose open-source implementation is available as part the VBA toolbox.