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A note on approximate Bayesian credible sets based on modified loglikelihood ratios

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  • Ventura, Laura
  • Ruli, Erlis
  • Racugno, Walter

Abstract

Higher-order asymptotic arguments for a scalar parameter of interest have been widely investigated for Bayesian inference. In this paper the theory of asymptotic expansions is discussed for a vector parameter of interest. A modified loglikelihood ratio is suggested, which can be used to derive approximate Bayesian credible sets with accurate frequentist coverage. Three examples are illustrated.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:11:p:2467-2472
    DOI: 10.1016/j.spl.2013.07.007
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    References listed on IDEAS

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    1. 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.
    2. Ib M. Skovgaard, 2001. "Likelihood Asymptotics," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(1), pages 3-32, March.
    3. T. J. Sweeting, 1999. "On the construction of Bayes–confidence regions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(4), pages 849-861.
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    Cited by:

    1. 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.

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