Testing equality of two functions using BARS

This article presents two methods of testing the hypothesis of equality of two functions H-0 : f(1) (t) = f(2)(t) for all t, in a generalized non-parametric regression framework using a recently developed generalized non-parametric regression method called Bayesian adaptive regression splines (BARS). Of particular interest is the special case of testing equality of two Poisson process intensity functions lambda(1)(t) = lambda(2)(t), which arises frequently in neurophysiological applications. The first method uses Bayes factors, and the second method uses a modified Hotelling T-2 test. Both methods are applied to the analysis of 347 motor cortical neurons and, for certain choices of test criteria, the two methods lead to the same conclusions for all but 7 neurons. A small simulation study of power indicates that the Bayes factor can be somewhat more powerful in small samples. The T-2-type test should be useful in screening large number of neurons for condition-related activity, while the Bayes factor will be especially helpful in assessing evidence in favour of H-0. Copyright (C) 2005 John Wiley & Sons, Ltd.