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

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.

The emphasis of this proposal is understanding, scientific understanding of the data generating mechanisms. This goal is distinct from much of machine learning and other types of data science, whose focus is typically prediction. Important though that is, in scientific research, the objectives are almost always understanding, from which causal predictions are an incidental product.

If the objectives of this proposal are achieved, it would be a significant theoretical and methodological breakthrough, putting UK statistics at the forefront and providing trustworthy methods for the discovery of new truth in the scientific and other domains. The impact of scientific discovery on society and the economy cannot be over emphasized.