Selective Inference

• Activity Number: 151
• Type: Invited
• Date/Time: Monday, July 30, 2012 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Yoav Benjamini*+
• Companies: Tel Aviv University

Abstract

Drawing inference on a selected subset of the parameters, a subset that is selected because the parameters within seem interesting after viewing the data, is the domain of selective inference. The inference can be in the form of hypotheses testing, point estimation or interval estimation.

I shall review some examples, making the point that selective inference is both common and unavoidable in modern scientific research, yet it is an acute problem that if unattended hampers the replicability of discoveries.

I shall discuss the False Discovery Rate and the False non-Coverage Rate as two examples of "assessing performance on the average over the selected", thereby addressing selective inference.

Using the latter concept I shall address at least two specific problems.

(1) Selecting a few "promising" families of hypotheses, out of the many considered, and testing the hypotheses within each family separately based on the same data

(2) Estimating confidence intervals for the selected large parameters, intervals that sometimes enjoy power to determine the sign almost as one-sided confidence intervals.