Bayesian Sample Size Determination for Binomial Proportions
Bayesian Sample Size Determination for Binomial Proportions
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DOI：
10.1214/08-ba310
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发表时间：
2008-01-01
影响因子：
4.4
通讯作者：
Wolfson, David B.
中科院分区：
文献类型：
--
作者：
M'Lan, Cyr E.;Joseph, Lawrence;Wolfson, David B.
本文提出了几个新的结果在贝叶斯样本大小确定估计二项比例，并提供了一个全面的比较概述的主题。我们使用广义版本的平均长度和平均覆盖标准，中位数长度和中位数覆盖标准，以及最差结果标准及其修改版本来研究二项样本量问题。我们比较了由最高后验密度和等尾可信区间得出的样本量。在某些情况下，我们首次推导出封闭形式的样本大小公式，在不可能的情况下，我们描述了各种数值方法。从蒙特卡罗模拟到更复杂的曲线拟合技术，三阶分析近似，以及精确但计算量更大的方法，这些方法的复杂性不等。我们比较了每个标准的不同计算方法的准确性和效率，并提出了哪些方法是首选的建议。最后，我们再次首次考虑围绕样本量选择的先验稳健性的问题。全文都有例子。
This paper presents several new results on Bayesian sample size determination for estimating binomial proportions, and provides a comprehensive comparative overview of the subject. We investigate the binomial sample size problem using generalized versions of the Average Length and Average Coverage Criteria, the Median Length and Median Coverage Criteria, as well as the Worst Outcome Criterion and its modified version. We compare sample sizes derived from highest posterior density and equal-tailed credible intervals. In some cases, we derive, for the first time, closed form sample size formulae, and where this is not possible, we describe various numerical approaches. These range in complexity from Monte Carlo simulations to more sophisticated curve fitting techniques, third order analystic approximations, and exact, but more computaionally-intensive, methods. We compare the accuracy and efficiency of the different computational methods for each of the criteria and make recommendations about which methods are preferred. Finally, we consider, again for the first time, issues surrounding prior robustness on the choice of sample size. Examples are given throughout on the text.