The random set approach to nontraditional measurements is rigorously Bayesian

Abstract

In several previous publications the first author has proposed a "generalized likelihood function" (GLF) approach for processing nontraditional measurements such as attributes, features, natural-language statements, and inference rules. The GLF approach is based on random set "generalized measurement models" for nontraditional measurements. GLFs are not conventional likelihood functions, since they are not density functions and their integrals are usually infinite, rather than equal to 1. For this reason, it has been unclear whether or not the GLF approach is fully rigorous from a strict Bayesian point of view. In a recent paper, the first author demonstrated that the GLF of a specific type of nontraditional measurement - quantized measurements - is rigorously Bayesian. In this paper we show that this result can be generalized to arbitrary nontraditional measurements, thus removing any doubt that the GLF approach is rigorously Bayesian. © 2012 Copyright Society of Photo-Optical Instrumentation Engineers (SPIE).