We consider Bayesian sample size determination using a criterion that utilizes the first two moments of the posterior variance. We study the resulting sample size in dependence on the chosen prior and explore the success rate for bounding the posterior variance below a prescribed limit under the true sampling distribution. Compared with sample size determination based on the average of the posterior variance the proposed criterion leads to an increase in sample size and significantly improved success rates. Generic asymptotic properties are proven, such as an asymptotic expression for the sample size and a sort of phase transition. Our study is illustrated using two real world datasets with Poisson and normally distributed data. Based on our results some recommendations are given.

我们考虑使用利用后方方差的前两个时刻的标准进行贝叶斯样本大小确定。我们根据选择的先验来研究结果样本大小，并探索在真实采样分布下将后验方差限制在规定限制以下的成功率。与基于后验方差的平均值确定样本量相比，所提出的标准导致样本量的增加和成功率的显着提高。证明了一般渐近性质，例如样本大小的渐近表达和某种相变。我们的研究使用两个具有Poisson和正态分布数据的现实世界数据集进行了说明。根据我们的结果，给出了一些建议。