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Coherent statistical inference and Bayes theorem. (English) Zbl 0742.62003

A suitable extension of the classical Bayes theorem relative to a finite number of alternatives is called by the authors a Bayesian algorithm. The main purpose of the present paper is to give sufficient conditions for the assessment of a coherent inference (in conformity with de Finetti’s theory) by means of a Bayesian algorithm.
Under some further hypotheses such inference is shown to be coherent also in the sense of D. Heath and W. Sudderth [ibid. 6, 333-345 (1978; Zbl 0385.62005)] and D. A. Lane and W. Sudderth [ibid. 11, 114-120 (1983; Zbl 0555.62008)]. Moreover, a characterization of coherent posteriors is given, together with some remarks concerning finitely additive conditional probabilities.

MSC:

62A01 Foundations and philosophical topics in statistics
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