Model selection and local geometry

Abstract

We consider problems in model selection caused by the geometry of models close to their points of intersection. In some cases-including common classes of causal or graphical models, as well as time series models- distinct models may nevertheless have identical tangent spaces. This has two immediate consequences: First, in order to obtain constant power to reject one model in favour of another we need local alternative hypotheses that decrease to the null at a slower rate than the usual parametric n -1/2 (typically we will require n -1/4 or slower); in other words, to distinguish between the models we need large effect sizes or very large sample sizes. Second, we show that under even weaker c..