Contemporary scientific research is a distributed, collaborative endeavor, carried out by teams of researchers, regulatory institutions, funding agencies, commercial partners, and scientific bodies, all interacting with each other and facing different incentives. To maintain scientific rigor, statistical methods should acknowledge this state of affairs. To this end, we study hypothesis testing when there is an agent (e.g., a researcher or a pharmaceutical company) with a private prior about an unknown parameter and a principal (e.g., a policymaker or regulator) who wishes to make decisions based on the parameter value. The agent chooses whether to run a statistical trial based on their private prior and then the result of the trial is used by the principal to reach a decision. We show how the principal can conduct statistical inference that leverages the information that is revealed by an agent's strategic behavior -- their choice to run a trial or not. In particular, we show how the principal can design a policy to elucidate partial information about the agent's private prior beliefs and use this to control the posterior probability of the null. One implication is a simple guideline for the choice of significance threshold in clinical trials: the type-I error level should be set to be strictly less than the cost of the trial divided by the firm's profit if the trial is successful.

翻译：当代科学研究是一种分布式、协作性活动，由研究团队、监管机构、资助机构、商业合作伙伴及科学团体共同开展，各方相互互动并面临不同的激励因素。为维护科学严谨性，统计方法应承认这一现状。为此，我们研究当存在一个对未知参数拥有私人先验信息的代理方（例如研究人员或制药公司）以及一个希望基于参数值做出决策的委托方（例如政策制定者或监管者）时的假设检验问题。代理方根据其私人先验信息决定是否开展统计试验，随后试验结果被委托方用于决策。我们展示了委托方如何利用代理方战略行为（即选择是否开展试验）所揭示的信息进行统计推断。具体而言，我们证明了委托方可以设计一种策略来揭示代理方私人先验信念的部分信息，并利用该信息控制原假设的后验概率。这一研究的实际意义在于为临床试验中显著性阈值的选择提供了简明指导：应使第一类错误率严格小于试验成本除以企业若试验成功所获利润的比值。