In complex research problems, selecting the parameters of interest after looking at the data is a common and unavoidable practice. However, if unattended, such selective inference can seriously distort the meaning of inferential statistics, and as a result hamper the replicability of scientific discoveries. This area of research has been attracting many statistical researchers in the last 15 years, and the methodologies developed are widely used across many branches of Science.
1. I shall discuss the problem of selective inference when facing multiplicity,
reviewing the basic problem, its relationship to the replicability problems in Science, and the more traditional approach of simultaneous inference.
2. We shall conduct an in-depth tour of the False Discovery Rate (FDR) and False Coverage Rate (FCR); Both the concepts and the particular methods will be discussed, including adaptive methods, all of which try to assure that inferential properties hold on the average over the selected. We shall discuss the connections between dependency assumptions and the validity of the methods, as well as more general resampling methods.
3. Some recent advances in addressing the problem of selective inference in complex research problems, e.g. testing hierarchical systems of hypotheses and related open problems.
4. We shall discuss a variety of approaches to addressing selective inference utilizing the selection rule, including the knockoff approach, the conditional approach and the simultaneous over the selected approach for addressing selective inference.

Knowledge of basic statistical inference ideas: testing, estimation and confidence intervals.  (preferably a course that includes Statistical Theory e.g. Mathematical Statistics, or Analysis of Variance, or linear models)

References will be given during the course.
Written summary of the material in the course will be distributed.