Borrowing Strength via Shape Constraints and Convex Optimization
Presented by Ivan MIZERA
Type: Oral presentation
Track: Plenary Talk
We discuss one instance of so-called "borrowing strength" in statistics, in the context of compound decision strategy also referred to as the empirical Bayes approach. We show how certain plausible qualitative restrictions (in the vein of monotonicity, convexity, logarithmic concavity and similar) are capable of regularizing (without introducing ambiguous tuning parameters) the otherwise ill-posed problem of estimating a probability density, or the subsequent decision rule, via maximum likelihood method. Then we illustrate how the proposed methods become practically feasible through modern convex optimization algorithms - and at the same time, how the (convex) optimization theory opens new perspectives in the topic. Some data from popular sports are used in the examples. Joint work with Roger Koenker (University of Illinois) and Mu Lin (University of Alberta).