When one compares one or more DCMs using the "Compare" feature in the DCM menu, the output involves two bar graphs, one supposedly showing the posterior probabilities of models from AIC and one from BIC. Similarly, the output in the Matlab command prompt window shows a Bayes factor computed according to both the AIC and the BIC. What confuses me is that, from what I have learned in statistics classes, the AIC and the BIC have nothing to do with posterior probabilities. They are only scalar numbers, "information criteria." How is it possible to calculate posterior probabilities "from" the AIC and BIC? What are the two graphs doing differently? Similarly, with the Bayes factors, sometimes it is possible to get that the AIC and the BIC "disagree" as to which of the two models being compared has more evidence for it. However, when they do not disagree, they always compute the same value for the Bayes factor. How can this be? If they are doing two different things, shouldn't it also be possible that they both compute different values for the Bayes factor and yet also agree as to which of the two models being compared has more evidence for it? This has never happened in my experience. In fact, from what I have learned, the AIC and the BIC have nothing to do with the computation of the Bayes factor either. So how is it possible to compute the Bayes factor "from" the AIC and BIC? What is SPM5 doing differently in each case?
I recently submitted a project for a statistics class using this, and I was unable to answer the above questions when challenged. So I have a grade hinging on any help I can get, since I was unable to find the answer in the Penny et al (2004) Neuroimage paper about comparing DCMs. Any help would be greatly appreciated. Thank you very much.
