Theoretical foundations of inference in the presence of large numbers of nuisance parameters

任何测量方法都应该被校准，或者至少不能被高度错误校准。统计理论确保了对推理方法的这种校准，这些方法是应用统计学家和科学家的关键工具，因此使这种程序适用于目的。具体地说，在假设的重复应用中，所提出的方法应该在一个小的真理窗口内给出答案。目前的研究是关于在存在所谓的滋扰参数的情况下，对感兴趣的关键量进行校准推断，如药物或治疗的效果。这些都是没有直接关系或科学相关性的方面，但需要这些方面来完成对物理、生物或社会学系统的理想化表示。当人们希望限制描述数据生成过程的方程中建模假设的强度时，它们中的大量就会自然而然地出现。在国家层面上，对支撑我们观察到的数据的科学或社会真理的更好理解，可以带来显著的长期经济效益。例如，它允许更有针对性地进行昂贵的医疗筛查或政府监管，并允许从对新药、治疗计划或疫苗有效性的研究中获得安全的结论。

Any method of measurement should be calibrated or at least not highly miscalibrated. Statistical theory ensures such calibration for methods of inference, crucial tools for applied statisticians and scientists, thus making such procedures suitable for purpose. Specifically, in hypothetical repeated application, the proposed methods should give an answer within a small window of the truth. The present research is about calibrated inference for key quantities of interest, like the effect of a drug or treatment, in the presence of so called nuisance parameters. These are aspects of no direct concern or scientific relevance, but that are needed to complete the idealized representation of the physical, biological or sociological system. Large numbers of them arise naturally when one wishes to limit the strength of modelling assumptions in the equations describing the data generating process.On a national level, improved understanding of the scientific or societal truths underpinning the data we observe allows significant long term economic benefits. For instance, it allows costly medical screening or government regulation to be better targeted, and allows secure conclusions to be obtained from, say, studies into the efficacy of new drugs, treatment programs or vaccines.