Efficiently Computing Minimax Expected-Size Confidence Regions

Abstract

Given observed data and a collection of parameterized candidate models, a 1 -- α confidence region in parameter space provides useful insight as to those models which are a good fit to the data, all while keeping the probability of incorrect exclusion below α. With complex models, optimally precise procedures (those with small expected size) are, in practice, difficult to derive; one solution is the Minimax Expected-Size (MES) confidence procedure. The key computational problem of MES is computing a minimax equilibria to a certain zero-sum game. We show that this game is convex with bilinear payoffs, allowing us to apply any convex game solver, including linear programming. Exploiting the sparsity of the matrix, along with using fast linear programming software, allows us to compute approximate minimax expected-size confidence regions orders of magnitude faster than previously published methods. We test these approaches by estimating parameters for a cosmological model.