Goodness of fit tests for nonincreasing densities on real positive data with nonparametric Bayesian methods

Abstract

In this paper‎, ‎we study a nonparametric Bayesian inference on the family of nonincreasing density functions on real positive data‎. ‎One interesting problem is the goodness of fit test in such a context‎. ‎In other words‎, ‎we consider nonparametric Bayesian testing on the family of nonincreasing density in this domain‎. ‎So‎, ‎we define nonparametric hypothesis testing and compare two different testing approaches‎. ‎The first approach is given based on the Bayes factor‎. ‎This approach is the well-known Bayesian approach for testing‎, ‎although its computation is complicated‎. ‎Decision-theoretic considerations with the loss function drive the second approach for a given distance‎. ‎This second approach has the advantage of considering the distance to the null hypothesis but needs the definition of a threshold‎. ‎When no threshold is known as a priori‎, ‎a possibility exists to calculate a p-value‎, ‎and the method becomes more complicated to compute‎. ‎We propose a hybrid algorithm to accelerate the computation of the p-value‎. ‎The comparison of both approaches is performed based on a simulation study.