About: Bayesian model reduction

Bayesian model reduction is a method for computing the evidence and posterior over the parameters of Bayesian models that differ in their priors. A full model is fitted to data using standard approaches. Hypotheses are then tested by defining one or more 'reduced' models with alternative (and usually more restrictive) priors, which usually – in the limit – switch off certain parameters. The evidence and parameters of the reduced models can then be computed from the evidence and estimated (posterior) parameters of the full model using Bayesian model reduction. If the priors and posteriors are normally distributed, then there is an analytic solution which can be computed rapidly. This has multiple scientific and engineering applications: these include scoring the evidence for large numbers o