Bayesian model comparison: a geometric, graphical approach

 

It is rare, in complex situations, for any proposed model to correspond exactly to the uncertainties in the problem. Therefore, it is often helpful to decompose a comparison between models into a sequence of individual comparisons expressing the practical differences between the specifications. Such a comparison may reveal that different aspects of the data appear to support different models, while some aspects of the data appear to contradict all suggested models. We shall describe a general geometric representation for the comparison of uncertainty specifications which is well suited to this approach to model comparison. This representation is naturally suited to graphical display. The approach is general, but is especially
well-suited to comparing alternative specifications for exchangeable multivariate samples, where the displays may be interpreted as multi-variable residual plots on carefully chosen axes of variation.

This is joint work with David Wooff