A Note on Optimal Sample Sizes in Compliance Tests Using a Formal Bayesian Decision-Theoretic Approach for Finite and Infinite Populations
采用形式化贝叶斯决策理论，在预算约束下最大化期望效用，研究审计中有限与无限总体模型的最优样本量，并基于线性损失函数和先验分布给出结果。
Recently, Godfrey and Andrews [1982], hereafter GA, compared sample size requirements in auditing using finite versus infinite Bayesian population models. They concluded that required sample sizes for finite population models would never be larger than those required for an infinite population, and that both Bayesian models require smaller sample sizes than classical procedures. However, neither GA nor prior researchers who have utilized informal Bayesian techniques (e.g., Felix and Grimlund [1977]) included possible loss functions in their analyses. Obviously, some loss function, whether stated explicitly or relied upon implicitly, must enter auditors' sample size determinations. In this paper we examine optimal sample sizes using a formal Bayesian decision-theoretic approach, in which auditors seek to maximize expected utility subject to a budgetary constraint. The results are presented for finite and infinite population models based on a linear loss function and the prior distribution mean error rates for audit populations taken from