## Departmental Colloquium

Ryan Martin

UIC

New foundations of statistical inference and fun with random sets

**Abstract:**In a statistical inference problem, the goal is to describe uncertainties about the truthfulness of various hypotheses after seeing data. There are now a variety of ways to do this, but none are fully satisfactory. In this talk, I will describe a brand new approach, what we call "inferential models" (IMs). The key idea is the introduction of an auxiliary variable connected with the observable data and parameter of interest. We employ random sets to predict the auxiliary variable, producing a belief and plausibility function pair on the parameter space that can be used to summarize uncertainty. I will show that a surprisingly simple "nestedness" condition on the random sets is both sufficient and, in a certain sense, necessary for the resulting IM to be "good." (This is joint work with Chuanhai Liu at Purdue.)

Friday April 19, 2013 at 3:00 PM in SEO 636