  This paper reviews recent developments in statistical structure learning;
namely, Bayesian model reduction. Bayesian model reduction is a method for
rapidly computing the evidence and parameters of probabilistic models that
differ only in their priors. In the setting of variational Bayes this has an
analytical solution, which finesses the problem of scoring large model spaces
in model comparison or structure learning. In this technical note, we review
Bayesian model reduction and provide the relevant equations for several
discrete and continuous probability distributions. We provide worked examples
in the context of multivariate linear regression, Gaussian mixture models and
dynamical systems (dynamic causal modelling). These examples are accompanied by
the Matlab scripts necessary to reproduce the results. Finally, we briefly
review recent applications in the fields of neuroimaging and neuroscience.
Specifically, we consider structure learning and hierarchical or empirical
Bayes that can be regarded as a metaphor for neurobiological processes like
abductive reasoning.
