Optimal Bayes procedures for selecting the better of two Bernoulli populations
type: Item
instance of: scholarly article
title: Optimal Bayes procedures for selecting the better of two Bernoulli populations
zbMATH Open document ID: 0622.62023
DOI: 10.1016/0378-3758(86)90106-0
author: Radhika V. Kulkarni
author: Vidyadhar G. Kulkarni
published in: Journal of Statistical Planning and Inference
publication date: 1987-01-01T00:00:00Z
review text: Let \(\pi_ 1\) and \(\pi_ 2\) be two Bernoulli populations with probabilities of success \(p_ 1\) and \(p_ 2\), respectively. The authors consider a class of sequential procedures C(n) for selecting the population with the larger success probability. The class C(n) is defined by a sampling rule R which requires that at most n observations be taken from any one of the two populations, and a stopping rule S which requires that the sampling be stopped at the first stage m at which either inequality \(z_{1,m}\geq z_{2,m}+n-n_{2,m}\) or \(z_{2m}\geq z_{1,m}+n-n_{1,m}\) holds, where \(n_{i,m}(z_{i,m})\) denotes the total number of observations (successes) from population \(\pi_ i\) \((i=1,2)\). At termination, the population with the longer number of successes is selected. Assuming that \(p_ 1\) and \(p_ 2\) have independent Beta prior densities an optimal procedure in C(n) is given which minimizes E(N), the expected total number of observations until the sampling terminates. Empirical procedures as approximations to the optimal Bayes procedure are given. It is conjectured that the empirical procedures which use identical symmetric Beta priors for \(p_ 1\) and \(p_ 2\) are minimax within the class C(n).
Mathematics Subject Classification ID: 62F07
Mathematics Subject Classification ID: 62L10
Mathematics Subject Classification ID: 62C12
Mathematics Subject Classification ID: 62L05
Mathematics Subject Classification ID: 62C10
zbMATH DE Number: 4009539
zbMATH Keywords: recursion equations
zbMATH Keywords: uniform prior distributions
zbMATH Keywords: clinical trials
zbMATH Keywords: adaptive sequential selection procedures
zbMATH Keywords: Bernoulli populations
zbMATH Keywords: larger success probability
zbMATH Keywords: stopping rule
zbMATH Keywords: independent Beta prior densities
zbMATH Keywords: expected total number of observations
zbMATH Keywords: Empirical procedures
zbMATH Keywords: approximations
zbMATH Keywords: optimal Bayes procedure
zbMATH Keywords: symmetric Beta priors
zbMATH Keywords: minimax
reviewed by: Khursheed Alam
MaRDI profile type: Publication
full work available at URL: 0378-3758(86)90106-0
OpenAlex ID: W1997467935
cites work: A monte carlo study of the performance of a closed adaptive sequential procedure for selecting the best bernoulli population
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cites work: Q3681720
cites work: Optimal properties of the Bechhofer-Kulkarni Bernoulli selection procedure
description: scientific article; zbMATH DE number 4009539