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

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