goodness of fit tests for nonincreasing densities on real positive data with nonparametric bayesian methods

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.