Denneberg, Dieter Conditioning (updating) non-additive measures. (English) Zbl 0812.90001 Ann. Oper. Res. 52, 21-42 (1994). Several update rules for non-additive probabilities, among them the Dempster-Shafer rule for belief functions and certain update rules in the spirit of Bayesian statistics with multiple prior probabilities, are reviewed, investigated and compared with each other. This is done within the unifying framework of general, nonadditive measure and integration theory. The methods exposed here are capable of generalizing conditional expectation of random variables to the submodular or supermodular case at least if the given algebra is finite. Reviewer: D.Denneberg Cited in 3 ReviewsCited in 27 Documents MSC: 91B06 Decision theory 28A12 Contents, measures, outer measures, capacities 62C10 Bayesian problems; characterization of Bayes procedures 28A25 Integration with respect to measures and other set functions Keywords:Choquet integral; update rules; Dempster-Shafer rule; belief functions; Bayesian statistics; nonadditive measure PDFBibTeX XMLCite \textit{D. Denneberg}, Ann. Oper. Res. 52, 21--42 (1994; Zbl 0812.90001) Full Text: DOI References: [1] A. Chateauneuf and J.-Y. Jaffray, Local Möbius transforms of monotone capacities, in:Uncertainty Measures, eds. Klement and Weber, to appear. [2] D. Denneberg,Lectures on Non-Additive Measure and Integral (Kluwer Academic, Boston, 1994). · Zbl 0826.28002 [3] R. Fagin and J.Y. Halpern, A new approach to updating beliefs, in:Proc. 6th Conf. on Uncertainty in AI (1990), and in: Uncertainty in Art. Int. 6 (1991) 347–374. · Zbl 0742.68067 [4] I. Gilboa and D. Schmeidler, Updating ambiguous beliefs, J. Econ. Theory 59 (1993) 33–49. · Zbl 0780.90001 · doi:10.1006/jeth.1993.1003 [5] Y. Jaffray, Bayesian updating and belief functions, IEEE Trans. Syst., Man Cybern. SMC-22 (1992) 1144–1152. · Zbl 0769.62001 · doi:10.1109/21.179852 [6] C. Sundberg and C. Wagner, Generalized finite differences and Bayesian conditioning of Choquet capacities, Adv. Appl. Math. 13 (1992) 262–272. · Zbl 0757.60001 · doi:10.1016/0196-8858(92)90012-L [7] P. Walley, Coherent lower (and upper) probabilities, Department of Statistics, University of Warwick (1981). [8] P. Walley,Statistical Reasoning with Imprecise Probabilities (Chapman and Hall, London, 1991). · Zbl 0732.62004 [9] L.A. Wasserman and J.B. Kadane, Bayes’ theorem for Choquet capacities, Ann. Statist. 18 (1990) 1328–1339. · Zbl 0736.62026 · doi:10.1214/aos/1176347752 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.