Introduction

Abstract

In practice, one is very often faced with a decision-making problem, i.e., selecting a course of action among several possibilities. For instance, in a digital communication system, one of several possible symbols is transmitted over a channel, we need to determine the symbol that was transmitted based on the received noisy observations. In a radar detection system, a decision based on the radar return is to be made regarding the presence or absence of a target. In a medical diagnosis problem, based on an electrocardiogram, one needs to determine if the patient has a heart attack. In a target recognition problem, one needs to identify the type of aircraft being detected based on some observed aircraft features. In all of the above practical applications, the common issue is to make a decision from several possibilities based on available noisy observations, where the truly present phenomenon cannot be observed directly. The branch of statistics dealing with these type of problems is known as statistical decision or hypothesis testing.