Controlling the degree of caution in statistical inference with the Bayesian and frequentist approaches as opposite extremes

DOI10.1214/12-EJS689zbMath1274.62052arXiv1109.5278OpenAlexW1971976127WikidataQ57826642 ScholiaQ57826642MaRDI QIDQ1950836

David R. Bickel

Publication date: 28 May 2013

Published in: Electronic Journal of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1109.5278

zbMATH Keywords

maximum entropyambiguityminimum cross entropyimprecise probabilityconfidence distributionmaxmin expected utilityrobust Bayesian analysisEllsberg paradoxconditional gamma-minimaxminimum divergenceconfidence posteriorobserved confidence levelminimum relative entropyblended inferenceminimum information for discrimination

Mathematics Subject Classification ID

Bayesian inference (62F15) Bayesian problems; characterization of Bayes procedures (62C10) Minimax procedures in statistical decision theory (62C20) Foundations and philosophical topics in statistics (62A01)

Related Items (8)

A frequentist framework of inductive reasoning ⋮ Reporting Bayes factors or probabilities to decision makers of unknown loss functions ⋮ A prior-free framework of coherent inference and its derivation of simple shrinkage estimators ⋮ Blending Bayesian and frequentist methods according to the precision of prior information with applications to hypothesis testing ⋮ Inference after checking multiple Bayesian models for data conflict and applications to mitigating the influence of rejected priors ⋮ Predictive measures of the conflict between frequentist and Bayesian estimators ⋮ Game-theoretic probability combination with applications to resolving conflicts between statistical methods ⋮ A note on fiducial model averaging as an alternative to checking Bayesian and frequentist models

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