The d-risk of Bayesian estimation for the probability of success in Bernoulli trials

N.F. Bilalova

Kazan Federal University, Kazan, 420008 Russia

E-mail: bnfnal@gmail.com

Received August 10, 2022

 

ORIGINAL ARTICLE

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DOI: 10.26907/2541-7746.2022.4.271-284

For citation: Bilalova N.F. The d-risk of Bayesian estimation for the probability of success in Bernoulli trials. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2022, vol. 164, no. 4, pp. 271–284. doi: 10.26907/2541-7746.2022.4.271-284. (In Russian)

 

Abstract

This article considers the problem of estimating the probability p of success in Bernoulli trials when it is a priori the smallest. Using the d-posterior approach to the problem of guaranteed statistical inference, a Bayesian estimation of p was performed for a special loss function of type 1-0 with the relative error restriction and the beta prior distribution of the estimated parameter. The d-risk of the Bayesian estimation was calculated, and the impossibility to design a d-guaranteed estimation procedure for a fixed amount of tests was revealed.

Keywords: Bernoulli trials, Bayesian probability estimation, beta prior distribution, d-risk estimation

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