Coherent statistical inference and Bayes theorem (Q1175410)

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 \textit{D. Heath} and \textit{W. Sudderth} [ibid. 6, 333-345 (1978; Zbl 0385.62005)] and \textit{D. A. Lane} and \textit{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.