Abstract: Statistical uncertainty has many sources. P-values and confidence intervals usually quantify the overall uncertainty, which may include variation due to sampling and uncertainty due to measurement error, among others. Practitioners might be interested in quantifying only one source of uncertainty. For example, one might be interested in the uncertainty of a regression coefficient of a fixed set of subjects, which corresponds to quantifying the uncertainty due to measurement error and ignoring the variation induced by sampling the covariates. In causal inference, it is common to infer treatment effects for a certain set of subjects, only accounting for uncertainty due to random treatment assignment. Motivated by these examples, we consider conditional inference for conditional parameters in parametric and semi-parametric models; where we condition on observed characteristics of a population. We discuss methods to obtain conditionally valid p-values and confidence intervals. Conditional p-values can be used to construct a hierarchy of statistical evidence that may help clarify the generalizability of a statistical finding. In addition, we will discuss preliminary results on how to conduct transfer learning of conditional parameters, with rigorous conditional guarantees.
This is ongoing work with Ying Jin.