贝叶斯样本量确定：抽样分布估计还是探索？

中文摘要 AI 辅助

在设计许多贝叶斯研究时，样本量的选择旨在获得足够的功效以拒绝零假设，或达到区间估计足够窄的期望概率。对于复杂模型的研究，确定最小合适样本量通常需要密集的蒙特卡洛模拟。一种基于模拟的策略来考虑样本量空间，涉及在不同样本量下估计后验摘要（如后验概率或区间估计长度）的抽样分布。另一种策略则通过随机求根在样本量空间上探索这些抽样分布，而不在任何给定样本量下估计后验摘要的完整抽样分布。这些竞争方法的性能可以通过它们在重复实施中样本量建议的蒙特卡洛抽样分布来评估。在本文中，我们从理论上推导了各种贝叶斯样本量确定方法的这些蒙特卡洛抽样分布。为了促进贝叶斯样本量确定的最佳实践，我们进行了广泛的数值研究，以估计抽样分布估计和探索方法的蒙特卡洛抽样分布，评估其偏差、精度以及对调参参数的敏感性。

英文摘要

To design many Bayesian studies, the sample size is chosen to attain sufficient power to reject a null hypothesis or a desired probability that an interval estimate is sufficiently narrow. Determining the minimum suitable sample size for studies with complex models typically requires intensive Monte Carlo simulation. One simulation-based strategy to consider the sample-size space involves estimating sampling distributions of posterior summaries, such as posterior probabilities or interval estimate lengths, at various sample sizes. Another strategy instead explores these sampling distributions via stochastic root finding over the sample-size space, where the entire sampling distribution of posterior summaries is not estimated at any given sample size. The performance of these competing approaches can be assessed using their Monte Carlo sampling distributions of sample size recommendations across repeated implementations. In this paper, we theoretically derive these Monte Carlo sampling distributions for various Bayesian sample size determination approaches. To promote best practices for Bayesian sample size determination, we conduct extensive numerical studies to estimate these Monte Carlo sampling distributions for the sampling distribution estimation and exploration approaches to assess their bias, precision, and sensitivity to tuning parameters.

发表机构

• The University of British Columbia（不列颠哥伦比亚大学）

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