ABSTRACT
This chapter provides the mathematical and statistical foundations for solving some problems. It explains the three basic formulations for the binary detection problem: Bayesian, minimax, and Neyman-Pearson. The chapter shows that in all cases the optimum detection rule is a Likelihood Ratio Test with possible randomization and Bayesian composite detection can be reduced to an equivalent simple detection problem. Detection problems arise in a number of engineering applications such as radar, communications, surveillance, and image analysis. Detection problems fall under the umbrella of statistical decision theory, where the goal is to make a right choice from a set of alternatives in a noisy environment. Detection problems are also referred to as hypothesis testing problems, with the understanding that each element of S corresponds to a hypothesis about the nature of the observations. In addition to Bayes and minimax approaches there are other criteria and techniques that are specific to special classes of decision-making problems.
