Bayesian model evidence for order selection and correlation testing

Model selection is a critical component of data analysis procedures, and is particularly difficult for small numbers of observations such as is typical of functional MRI datasets. In this paper we derive two Bayesian evidence-based model selection procedures that exploit the existence of an analytic form for the linear Gaussian model class. Firstly, an evidence information criterion is proposed as a model order selection procedure for auto-regressive models, outperforming the commonly employed Akaike and Bayesian information criteria in simulated data. Secondly, an evidence-based method for testing change in linear correlation between datasets is proposed, which is demonstrated to outperform both the traditional statistical test of the null hypothesis of no correlation change and the likelihood ratio test.