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活动，由研究团队、监管机构、资助机构、商业伙伴及科学团体共同参与，各方相互影响并面临不同激励。为维护科学严谨性，统计方法应充分认识这一现实。为此，我们研究当存在一个持有未知参数先验信念的代理人（如研究者或制药公司）和另一个希望基于参数值做决策的委托人（如政策制定者或监管机构）时的假设检验问题。代理人根据其私有先验选择是否进行统计试验，试验结果随后被委托人用于决策。我们展示了委托人如何利用代理人策略行为（即是否进行试验的选择）所揭示的信息进行统计推断。具体而言，我们证明了委托人可以设计一种策略，以部分揭示代理人先验信念的私有信息，并据此控制零假设的后验概率。其一个实际应用是为临床试验显著性阈值的选择提供简明准则：第一类错误水平应严格低于试验成本与公司试验成功时的利润之比。