Optimal Properties of the Bechhofer-Kulkarni Bernoulli Selection Procedure
Bechhofer–Kulkarni伯努利总体选择程序的最优性质AI 解读 ↓
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Bechhofer–Kulkarni伯努利总体选择程序的最优性质
- 研究问题
- 从多个伯努利总体中选择成功概率最高者时，如何保持既定正确选择概率，并在受限自适应序贯程序类内减少期望观测数？
- 方法与思路
- 作者用新的证明方法研究既有程序在两个及更多总体下的最优性质，并为至少三个总体提出新的选择程序。
- 材料陈述的贡献
- 摘要称加强了既有结果与猜想，并证明新程序在所有成功概率较小时最小化终止抽样所需的期望总观测数。
- 阅读关注点
- 应核对允许比较的程序类、正确选择概率的约束、逐总体观测上限，以及成功概率较小的精确定义和最优性范围。
- 阅读边界
- 材料为OpenAlex索引摘要，稿件版本未注明；不能将受限程序类内或小成功概率下的最优性推广至任意抽样策略。
原文摘要
In a recent article Bechhofer and Kulkarni proposed a class of closed adaptive sequential procedures for selecting that one of $k \geq 2$ Bernoulli populations with the largest single-trial success probability. These sequential procedures which take no more than $n$ observations from any one of the $k$ populations achieve the same probability of a correct selection as does a single-stage procedure which takes exactly $n$ observations from every one of the $k$ populations. In addition, they often require substantially less than a total of $kn$ observations to terminate sampling. Amongst other problems, Bechhofer and Kulkarni considered the problem of devising a procedure within this class which minimizes the expected total number of observations to terminate sampling. For their proposed procedure they cited several optimality properties for the case $k = 2$ and conjectured additional optimality properties for the case $k \geq 3$. In this article we use a new method of proof to establish stronger results than those cited by Bechhofer and Kulkarni for the case $k = 2$, and prove stronger results than those conjectured for $k \geq 3$. We also describe a new procedure for $k \geq 3$ and prove that it minimizes the expected total number of observations to terminate sampling when all of the success probabilities are small.