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).