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

Jean-Pierre Florens (), Jean-Francois Richard and Jean-Marie Rolin
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Jean-Pierre Florens: Université Toulouse Capitole, Toulouse School of Economics
Jean-Marie Rolin: Université Catholique de Louvain, Institut de Statistique

Chapter Chapter 7 in Nonparametric Bayesian Inference, 2024, pp 143-162 from Springer

Abstract: Abstract Encompassing tests of a model M 0 $$M_0$$ are based upon the notion that M 0 $$M_0$$ ought to be able to account for results derived upon alternative models. Within a Bayesian framework, posterior distributions obtained under an alternative model M 1 $$M_1$$ are explicitly compared with posterior distributions obtained within M 0 $$M_0$$ by means of a suitable “transition” distribution for the parameters of M 1 $$M_1$$ conditionnally on those of M 0 $$M_0$$ . In our chapter, we propose a generic Bayesian procedure for testing the capabilities of a parametric model M 0 $$M_0$$ to encompass a wide range of inferential results derived under a nonparametric alternative M 1 $$M_1$$ . By combining the use of Dirichlet prior measures on M 1 $$M_1$$ with that of Monte Carlo simulation techniques, we develop exact operational and highly flexible Bayesian encompassing test procedures of M 0 $$M_0$$ relative to M 1 $$M_1$$ . An application to an exponential lifetime model M 0 $$M_0$$ illustrates the performance of our procedure.

Date: 2024
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Related works:
Working Paper: Bayesian Encompassing Specification Tests of a Parametric Model Against a Non Parametric Alternative (1996)
Working Paper: Bayesian Encompassing Specification Tests of a Parametric Model Against a Non Parametric Alternative (1996)
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DOI: 10.1007/978-3-031-61329-6_7

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