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Approximate Bayesian computation with modified log-likelihood ratios

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Abstract

The aim of this contribution is to discuss approximate Bayesian computation based on the asymptotic theory of modified likelihood roots and log-likelihood ratios. Results on third-order approximations for univariate posterior distributions, also in the presence of nuisance parameters, are reviewed and the computation of asymptotic credible sets for a vector parameter of interest is illustrated. All these approximations are available at little additional computational cost over simple first-order approximations. Some illustrative examples are discussed, with particular attention to the use of matching priors.

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Acknowledgments

This work was supported by a grant from the University of Padua (Progetti di Ricerca di Ateneo 2011) and by the Cariparo Foundation Excellence-grant 2011/2012.

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Authors and Affiliations

  1. Department of Statistical Sciences, University of Padova, Padua, Italy

    Laura Ventura

  2. Department of Statistics, University of Toronto, Toronto, ON, Canada

    Nancy Reid

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  1. Laura Ventura
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  2. Nancy Reid
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Correspondence to Laura Ventura.

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Ventura, L., Reid, N. Approximate Bayesian computation with modified log-likelihood ratios. METRON 72, 231–245 (2014). https://doi.org/10.1007/s40300-014-0041-4

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