Elements of Detection Theory

Abstract

There are many practical situations in which one is faced with a decision-making problem, i.e., the problem of choosing a course of action from several possibilities. For example, in a radar detection context, a decision is to be made regarding the presence or absence of a target based on the radar return. In a digital communication system, one of several possible waveforms is transmitted over a channel. Based on the received noisy observation, we need to determine the symbol that was transmitted. In a biomedical application, based on a smear of human tissue, one needs to determine if it is cancerous. In a pattern recognition problem, one needs to determine the type of aircraft being observed based on some aircraft features. In all of the above applications, the common underlying problem is to make a decision among several possible choices. This is carried out based on available noisy observations. The branch of statistics dealing with these types of problems is known as statistical decision theory or hypothesis testing. In the context of radar and communication theory, it is known as detection theory.