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A Quasi likelihood approximation of posterior distributions for likelihood-intractable complex models

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Abstract

Complex models typically involve intractable likelihood functions which, from a Bayesian perspective, lead to intractable posterior distributions. In this context, Approximate Bayesian computation (ABC) methods can be used in order to obtain a valid posterior approximation. However, when simulation from the model is computationally demanding, then the ABC approach may be cumbersome. We discuss an alternative method, where the intractable likelihood is approximated by a quasi-likelihood calculated through an algorithm that is reminiscent of the ABC. The proposed approximation method requires less computational effort than ABC. An extension to multiparameter models is also considered and the method is illustrated by several examples.

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Acknowledgments

Maria Eugenia Castellanos was partially supported by Ministerio de Ciencia e Innovación grant MTM2010-19528 and the visiting professor program of the Regione Autonoma della Sardegna. Stefano Cabras has been partially supported by Ministerio de Ciencia e Innovación grant ECO2012-38442, RYC-2012-11455 and Erlis Ruli were partially supported by Ministero dell’Istruzione, dell’Univesità e della Ricerca of Italy.

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Authors and Affiliations

  1. Department of Mathematics, Università di Cagliari, Cagliari, Italy

    Stefano Cabras

  2. Department of Statistics, Universidad Carlos III de Madrid, Madrid, Spain

    Stefano Cabras

  3. Department of Statistics and Operations Research, Universidad Rey Juan Carlos, Madrid, Spain

    María Eugenia Castellanos

  4. Department of Statistics, Università di Padova, Padova, Italy

    Erlis Ruli

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  1. Stefano Cabras
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  2. María Eugenia Castellanos
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  3. Erlis Ruli
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Correspondence to Stefano Cabras.

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Cabras, S., Castellanos, M.E. & Ruli, E. A Quasi likelihood approximation of posterior distributions for likelihood-intractable complex models. METRON 72, 153–167 (2014). https://doi.org/10.1007/s40300-014-0040-5

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