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Pseudo-Likelihoods for Bayesian Inference

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Topics on Methodological and Applied Statistical Inference

Part of the book series: Studies in Theoretical and Applied Statistics ((STASSPSS))

Abstract

The interplay between Bayesian and frequentist inference can play a remarkable role in order to address some theoretical and computational drawbacks, due to the complexity or misspecification of the model, or to the presence of many nuisance parameters. In this respect, in this paper we review the properties and applications of the so-called pseudo-posterior distributions, i.e., posterior distributions derived from the combination of a pseudo-likelihood function with suitable prior information. In particular, we illustrate the various notions of pseudo-likelihood highlighting their use in the Bayesian framework. Moreover, we show the simple but effective application of pseudo-posterior distributions in three challenging examples.

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Acknowledgments

This work was supported by a grant from the University of Padua (Progetti di Ricerca di Ateneo 2013) and by the grant Progetto di Ricerca di Base, Legge Regionale Sardegna. 7/2007-2012.

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Authors and Affiliations

  1. Department of Statistics, University of Padova, Padova, Italy

    Laura Ventura

  2. Department of Mathematics and Informatics, University of Cagliari, Cagliari, Italy

    Walter Racugno

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  1. Laura Ventura
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  2. Walter Racugno
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Correspondence to Laura Ventura .

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Editors and Affiliations

  1. Universita delgi Studi G. "d'Annunzio" chieti pescara, Pescara, Italy

    Tonio Di Battista

  2. Statistics & Operations Research, University of Granada, Granada, Spain

    Elías Moreno

  3. Department of Mathematics, University of Cagliari Department of Mathematics, Cagliari, Italy

    Walter Racugno

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Ventura, L., Racugno, W. (2016). Pseudo-Likelihoods for Bayesian Inference. In: Di Battista, T., Moreno, E., Racugno, W. (eds) Topics on Methodological and Applied Statistical Inference. Studies in Theoretical and Applied Statistics(). Springer, Cham. https://doi.org/10.1007/978-3-319-44093-4_19

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