Bayesian Encompassing Specification Tests of a Parametric Model Against a Non Parametric Alternative

An encompassing test between two models is based on the idea that the fist model is able to explain the inference obtained by the second model. In a Bayesian framework, the posterior distribution of the second model will then be compared to the posterior distribution built in the first model t hrough a distribution on the parameter of the second model conditionally on the parameter of the first model. Such a strategy is used to test a parametric model against a non parametric one. This strategy is in particular justifed by the inadequacy of usual tests as posterior odds. But the implementation of encompassing tests can only be made thanks to simulation techniques which intensively use representations of Dirichlet measures.