Determining an appropriate sample size is a critical element of study design, and the method used to determine it should be consistent with the planned analysis. When the planned analysis involves Bayes factor hypothesis testing, the sample size is usually desired to ensure a sufficiently high probability of obtaining a Bayes factor indicating compelling evidence for a hypothesis, given that the hypothesis is true. In practice, Bayes factor sample size determination is typically performed using computationally intensive Monte Carlo simulation. Here, we summarize alternative approaches that enable sample size determination without simulation. We show how, under approximate normality assumptions, sample sizes can be determined numerically, and provide the R package bfpwr for this purpose. Additionally, we identify conditions under which sample sizes can even be determined in closed-form, resulting in novel, easy-to-use formulas that also help foster intuition, enable asymptotic analysis, and can also be used for hybrid Bayesian/likelihoodist design. Furthermore, we show how in our framework power and sample size can be computed without simulation for more complex analysis priors, such as Jeffreys-Zellner-Siow priors or nonlocal normal moment priors. Case studies from medicine and psychology illustrate how researchers can use our methods to design informative yet cost-efficient studies.

翻译：确定合适的样本量是研究设计的关键要素，所采用的方法应与计划分析保持一致。当计划分析涉及贝叶斯因子假设检验时，通常需要确定样本量以确保在假设成立的情况下，以足够高的概率获得能够为假设提供有力证据的贝叶斯因子。在实践中，贝叶斯因子样本量确定通常通过计算密集的蒙特卡洛模拟进行。本文总结了无需模拟即可实现样本量确定的替代方法。我们展示了在近似正态性假设下如何通过数值方法确定样本量，并为此提供了R软件包bfpwr。此外，我们确定了样本量甚至可以通过闭式解确定的条件，从而推导出新颖且易于使用的计算公式。这些公式不仅有助于培养直觉理解、支持渐近分析，还可用于混合贝叶斯/似然主义研究设计。进一步地，我们展示了在该框架下如何无需模拟即可计算更复杂分析先验（如Jeffreys-Zellner-Siow先验或非局部正态矩先验）的功效与样本量。来自医学和心理学的案例研究说明了研究者如何运用我们的方法设计信息充分且成本高效的研究。