Abstract
Noteworthy connections among conglomerability, countable additivity and coherence are discussed in detail, reaching the conclusion that nonconglomerable conditional probabilities must not be doomed and play a significant role in statistical inference.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Apostol T (1963) Mathematical analysis: a modern approach to advanced calculus. Addison-Wesley, Reading
Berti P, Rigo P (2002) On coherent conditional probabilities and disintegrations. Ann Math Artif Intell 35:71–82
Bouchon-Meunier B, Coletti G, Marsala C (2002) Independence and possibilistic conditioning. Ann Math Artif Intell 35:63–69
Coletti G, Scozzafava R (1993) Qualitative Bayesian inference. In: Proceedings of the section on “Bayesian Statistical Science” (San Francisco), Amer Statistcal Association, Alexandra, pp 184–191
Coletti G, Scozzafava R (1996) Characterization of coherent conditional probabilities as a tool for their assessment and extension. Int J Uncertainty Fuzziness Know Based Syst 4:103–127
Coletti G, Scozzafava R (1999) Conditioning and Inference in intelligent systems. Soft Comput 3:118–130
Coletti G, Scozzafava R (2000) The role of coherence in eliciting and handling “imprecise” probabilities and its application to medical diagnosis. Inf Sci 130:41–65
Coletti G, Scozzafava R (2001) From conditional events to conditional measures: a new axiomatic approach. Ann Math Artif Intell 32:373–392
Coletti G, Scozzafava R (2002) Probabilistic logic in a coherent setting (Trends in logic, n.15). Kluwer, Dordrecht, Boston, London
de Finetti B (1928) Sulle probabilità numerabili e geometriche. Rend Reale Ist. Lombardo Sci Lett 61:817–824
de Finetti B (1949) Sull’impostazione assiomatica del calcolo delle probabilità. Annali Univ. Trieste 19: 3–55 (Engl. transl.: Ch.5 in Probability, Induction, Statistics. Wiley, London, 1972)
de Finetti B (1970) Teoria della probabilità. Einaudi, Torino (Engl. transl.: Theory of Probability, Vol 1 and 2. Wiley, Chichester, 1974)
Fan K (1956) On systems of linear inequalities. In: Linear inequalities and related systems, Annals of Mathematical Studies, vol 38. Princeton University Press, New Jersey
Gale D (1960) The theory of linear economic models. MacGraw-Hill, New York
Holzer S (1985) On coherence and conditional prevision. Boll Un Mat Ital (6)4:441–460
Lehman RS (1955) On confirmation and rational betting. J Symbolic Logic 20:251–262
Neveu J (1965) Mathematical foundations of the calculus of probability. Holden-Day, San Francisco
Regazzini E (1985) Finitely additive conditional probabilities. Rend Sem Mat Fis Milano 55:69–89
Scozzafava R (1981) Non conglomerability and the first digit problem. Statistica 41:561–565
Walley P (1991) Statistical reasoning with imprecise probabilities. Chapman and Hall, London
Williams PM (1975) Notes on conditional previsions. School of Mathematical and Physical Sciences, working paper, The University of Sussex
Williams PM (1976) Indeterminate probabilities. In: Przelecki M, Szaniawski K, Vojcicki R (eds) Formal methods in the methodology of empirical sciences. Reidel, Dordrecht, pp 229–246
Author information
Authors and Affiliations
Corresponding author
Additional information
Extended and updated version of a contributed paper presented at the International Conference on “Information Processing and Management of Uncertainty in knowledge-based systems”, IPMU 2004, Perugia, Italy.
Rights and permissions
About this article
Cite this article
Coletti, G., Scozzafava, R. Nonconglomerative coherent conditional probabilities in statistical inference. Stat. Meth. & Appl. 16, 229–243 (2007). https://doi.org/10.1007/s10260-006-0026-4
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10260-006-0026-4