Gaussian Processes for Bayesian hypothesis tests on regression functions

Gaussian processes have been used in different application domains such as classification, regression etc. In this paper we show that they can also be employed as a universal tool for developing a large variety of Bayesian statistical hypothesis tests for regression functions. In particular, we will use GPs for testing whether (i) two functions are equal; (ii) a function is monotone (even accounting for seasonality effects); (iii) a function is periodic; (iv) two functions are proportional. By simulation studies, we will show that, beside being more flexible, GP tests are also competitive in terms of performance with state-of-art algorithms.