Exact, Recursive, Inference of Event Space Probability Law for Discrete Random Sets with Applications

Abstract

In this paper we extend Choquet's result to obtain a recursive procedure for the computation of the underlying event-space probability law for Discrete Random Sets, based on Choquet's capacity functional. This is an important result, because it paves the way for the solution of statistical inference problems for Discrete Random Sets. As an example, we consider the Discrete Boolean Random Set with Radial Convex Primary Grains model, compute its capacity functional, and use our procedure to obtain a recursive solution to the problem of M-ary MAP hypothesis testing for the given model. The same procedure can be applied to the problem of ML model fitting. Various important probability functionals are computed in the process of obtaining the above results.