Confidence-credible intervals

Frequentist and Bayesian approaches for interval estimation usually produce conflicting results if applied to analyze the same data set. Paradoxically, there is no unanimity in the literature on whether frequentist and Bayesian approaches are indeed concurrent theories. Thus, a fundamental question...

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Bibliographic Details
Published inCommunications in statistics. Theory and methods Vol. 51; no. 9; pp. 2783 - 2802
Main Authors Silva, Ivair R., Oliveira, Dionatan W. R.
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 25.03.2022
Taylor & Francis Ltd
Subjects
Bayesian analysis
Coverage probability
credible intervals
Questions
State space models
statistical fundamentals
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Summary:Frequentist and Bayesian approaches for interval estimation usually produce conflicting results if applied to analyze the same data set. Paradoxically, there is no unanimity in the literature on whether frequentist and Bayesian approaches are indeed concurrent theories. Thus, a fundamental question arises: frequentist and Bayesian approaches for interval estimation could be somehow reconciled? This paper offers an affirmative response for this question. Furthermore, we introduce a reconciling solution based on a hybrid frequentist-Bayesian interval estimator, the 'confidence-credible interval'. The hybrid approach is simple and intuitive. It is also comprehensive in the sense of being applicable for any data probability distribution/likelihood shape, and for arbitrary prior distributions. An intensive simulation study shows the performance of the new methodology for the Gaussian and the Gamma distributions. The proposed method is illustrated through an application using real data in the light of state space models.
ISSN:0361-0926
1532-415X
DOI:10.1080/03610926.2020.1780447