To make calculations in the Bayesian analysis, the formalism of which is based on the layering of a probability measure defined on the product of measurable spaces, it is useful to have a summary of the properties of this layering. In this paper we formulate and prove those of them that are used in calculations more often than others. Particularly, we prove Hoeffding-type inequalities using direct elementary techniques.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
J. Neveu, Bases Mathématiques du Calcul des Probabilités, Masson, Paris (1964).
J.-R. Barra, Notions Fondamentales de Statistique Mathématique, DNOD, Paris (1971).
A. M. Yaglom, “Random function,” in: Great Russian Encyclopaedia, Encyclopaedia: Probability and Mathematical Statistics, (1999), Nauka, Moscow, pp. 589–590.
A. N. Shiryayev, Probability, Springer, Berlin (1996).
N. Bourbaki, Théorie des ensembles, Springer, Berlin (1958).
I. Dieudonne, “Sur le théorème de Radon–Nikodym,” Ann. Univ. Grenoble, 23, 25–53 (1948).
V. A. Lebedev, Martingales, Convergence of Probability Measures and Stochastic Equations, MAI, Moscow (1996).
W. Hoeffding, “Masstabvariante korrelations theorie,” Sehr. Math. Inst. Berlin, 5, 191–233 (1940).
V. M. Zolotarev, Modern Theory of Summation of Independent Random Variables, VSP, Utrech (1999).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Statisticheskie Metody Otsenivaniya i Proverki Gipotez, Vol. 20, pp. 149–169, 2007
Rights and permissions
About this article
Cite this article
Ivanov, I.V. On Bayes Equality and Related Issues. J Math Sci 228, 481–494 (2018). https://doi.org/10.1007/s10958-017-3637-4
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-017-3637-4