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Approximate Bayesian computation with modified log-likelihood ratios

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  • Laura Ventura
  • Nancy Reid

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. Copyright Sapienza Università di Roma 2014

Suggested Citation

  • Laura Ventura & Nancy Reid, 2014. "Approximate Bayesian computation with modified log-likelihood ratios," METRON, Springer;Sapienza Università di Roma, vol. 72(2), pages 231-245, August.
    • Handle: RePEc:spr:metron:v:72:y:2014:i:2:p:231-245
    DOI: 10.1007/s40300-014-0041-4
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    References listed on IDEAS

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    1. Ventura, Laura & Ruli, Erlis & Racugno, Walter, 2013. "A note on approximate Bayesian credible sets based on modified loglikelihood ratios," Statistics & Probability Letters, Elsevier, vol. 83(11), pages 2467-2472.
    2. Ventura, Laura & Cabras, Stefano & Racugno, Walter, 2009. "Prior Distributions From Pseudo-Likelihoods in the Presence of Nuisance Parameters," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 768-774.
    3. Ventura, Laura & Sartori, Nicola & Racugno, Walter, 2013. "Objective Bayesian higher-order asymptotics in models with nuisance parameters," Computational Statistics & Data Analysis, Elsevier, vol. 60(C), pages 90-96.
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    Cited by:

    1. Erlis Ruli & Laura Ventura, 2021. "Can Bayesian, confidence distribution and frequentist inference agree?," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(1), pages 359-373, March.

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