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

In: Nonparametric Bayesian Inference

Author

Listed:
  • Jean-Pierre Florens

    (Université Toulouse Capitole, Toulouse School of Economics)

  • Jean-François Richard

    (University of Pittsburgh, Department of Economics)

  • Jean-Marie Rolin

    (Université Catholique de Louvain, Institut de Statistique)

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.

Suggested Citation

  • Jean-Pierre Florens & Jean-François Richard & Jean-Marie Rolin, 2024. "Bayesian Encompassing Specification Tests of a Parametric Model Against a Nonparametric Alternative," Springer Books, in: Jean-Pierre Florens & Michel Mouchart (ed.), Nonparametric Bayesian Inference, chapter 0, pages 143-162, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-61329-6_7
    DOI: 10.1007/978-3-031-61329-6_7
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