SEQUENTIAL CLASSIFICATION ON PARTIALLY ORDERED SETS

Curtis Tatsuoka and Thomas Ferguson

The George Washington University, and University of California at Los Angeles

Abstract

A general theorem on asymptotically optimal sequential selection of experiments is presented and applied to a Bayesian classification problem when the parameter space is a finite partially ordered set. The main results include establishing conditions under which the posterior probability of the true state converges to one almost surely, and determining optimal rates of convergence. Properties of various classes of experiment selection rules are explored.