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Can Bayesian, confidence distribution and frequentist inference agree?

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  • Erlis Ruli

    (University of Padova)

  • Laura Ventura

    (University of Padova)

Abstract

We discuss and characterise connections between frequentist, confidence distribution and objective Bayesian inference, when considering higher-order asymptotics, matching priors, and confidence distributions based on pivotal quantities. The focus is on testing precise or sharp null hypotheses on a scalar parameter of interest. Moreover, we illustrate that the application of these procedures requires little additional effort compared to the application of standard first-order theory. In this respect, using the R software, we indicate how to perform in practice the computation with three examples in the context of data from inter-laboratory studies, of the stress–strength reliability, and of a growth curve from dose–response data.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stmapp:v:30:y:2021:i:1:d:10.1007_s10260-020-00520-y
    DOI: 10.1007/s10260-020-00520-y
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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.
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    6. Min-ge Xie & Kesar Singh, 2013. "Confidence Distribution, the Frequentist Distribution Estimator of a Parameter: A Review," International Statistical Review, International Statistical Institute, vol. 81(1), pages 3-39, April.
    7. 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.
    8. M. Madruga & Luis Esteves & Sergio Wechsler, 2001. "On the bayesianity of pereira-stern tests," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 10(2), pages 291-299, December.
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