This article is cited in 1 paper

Probabilistic models

Interval estimation based on the principle of consistency

S. I. Gurov

Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics

Abstract: A new method to specify an a priori distribution when using the Bayes approach is proposed based on the consistency principle. This principle is referred to as the consistency principle, since it assumes, on the one hand, the uniformity of the a priori densities and the likelihood function of the parameter and, on the other hand, the equality of the frequency and Bayes point estimates. The notions of the fiducial Fischer theory are used to determine the class of the a priori distributions. Thus, we propose the consistency principle unifying the frequency, Bayes, and fiducial approaches of mathematical statistics. The method is used to solve the problem of interval estimations of the classification error probability in various statistical models (binomial, polynomial, Poisson and normal).

Keywords: distribution, Bayes approach, consistency principle, interval estimation.

UDC: 681.513.7

Received: 10.03.2008
Revised: 06.06.2008

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