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An introduction to the imprecise Dirichlet model for multinomial data. (English) Zbl 1066.62003
Summary: The imprecise Dirichlet model (IDM) was recently proposed by P. Walley [J. R. Stat. Soc., Ser. B 58, 3–57 (1996; Zbl 0834.62004); Statistical reasoning with imprecise probabilities (1991; Zbl 0732.62004)] as a model for objective statistical inference from multinomial data with chances \(\theta\). In the IDM, prior or posterior uncertainty about \(\theta\) is described by a set of Dirichlet distributions, and inferences about events are summarized by lower and upper probabilities. The IDM avoids shortcomings of alternative objective models, either frequentist or Bayesian. We review the properties of the model, for both parametric and predictive inferences, and some of its recent applications to various statistical problems.

MSC:
62A01 Foundations and philosophical topics in statistics
62F15 Bayesian inference
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