Seminario Sparsity, signal detection and false discovery rates

Relatore: Peter McCullagh (University of Chicago)

Abstract:

Historically, the Gaussian signal-plus-noise model arises in at least two areas of scientific research, but with different goals achieved by substantially different techniques. The problem in astronomy is to estimate the distance to several hundred nearby stars using the method of parallax: All parallaxes are positive, but the measured values (in parsecs) may be negative. With the help of Eddington, Dyson (1926) showed how to correct the observations so that the corrected values are positive. Eddington's correction has been rediscovered in the statistics literature as Tweedie's formula. In a retrospective case-control study, the problem is to identify genes that are `active' in the sense of being associated with disease. This is chiefly a problem of detection rather than estimation. The genomics literature focuses on the `local false discovery rate', which is the conditional probability that the discovery is false. Unfortunately, the literature does not identify the event that corresponds to a false discovery. A gene whose contribution is null or zero is certainly false or inactive.  But an inactive gene may have a non-null signal X>0. This talk shows how to define "activity" as a Bernoulli variable such that inactivity corresponds to false discovery. Under sparsity assumptions, we show that the local false discovery rate is approximately equal to Pr(|X| < 1.377/|Y| | Y). Based on joint work with D. Xiang and N. Ignatiadis

Organizzatore: Carlo Trivisano