Dynamic causal modeling: Difference between revisions

Revision as of 17:29, 17 May 2018

Revision as of 17:45, 17 May 2018

Line 81:

== Example ==

[[File:Example full and reduced priors.png|thumb|Example priors. In a 'full' model, left, a parameter has a Gaussian prior with mean 0 and standard deviation 0.5. In a 'reduced' model, right, the same parameter has prior mean zero and standard deviation 1/1000. Bayesian model reduction enables the evidence and parameter(s) of the reduced model to be derived from the evidence and parameter(s) of the full model.]]

Consider a model with a parameter <math>\theta</math> and Gaussian prior <math>p(\theta)=N(0,0.5^2)</math>, which is the Normal distribution with mean zero and standard deviation 0.5 (illustrated in the Figure, left). This prior says that without any data, this parameter is expected to have value zero, but we are willing to entertain positive or negative values (with a 99% confidence interval [-1.16 1.16]). This model is fitted to the data to provide an estimate of the parameter <math>q(\theta)</math> and the model evidence <math>p(y)</math>.