关于样本容量、验前信息与Bayes决策风险的若干讨论

针对工程实际中所普遍存在的小子样问题,分析验前信息和样本容量大小对Bayes决策的影响.将验前费用和试验费用引入到损失函数中,研究样本容量大小、验前信息以及Bayes决策风险三者之间的关系.并在给定决策风险上限和总费用的条件下,理论上推导样本容量大小、验前信息的可信度、总费用以及Bayes决策风险关系式,从而为小子样条件下,找到验前信息可信度的保证下限提供了理论依据.

A Few Discussion of Samples,a Prior Information and Bayesian Statistical Decision

Considering the problem of small samples in engineering,we analyze the effect ofa priori information credibility and samples in Bayesian statistical decision.The relation of samples,a priori information and Bayesian statistical decision adventure is studied by introducing a priori cost and testing into the Bayesian loss function.Under the condition of given the decision adventure limitation and total cost,two relation formula about samples,a priori information credibility,total cost and Bayesian statistical decision adventure have been deduced on theory.Therefore,under the condition of small samples,a kind of theorical method to find the bottomline of a priori information credibility is presented.