Detection Statistics

Abstract

Applied probability theory forms the basis for the analysis of signals from nuclear detection equipment. Both classical and Bayesian statistical methods have been applied to nuclear detection problems, and an introduction to the concepts important to these approaches is presented. The statistics of nuclear counting is presented from the classical probability calculations for independent random events, leading to Poisson and Gaussian statistical models. The concept of error propagation, where many concatenated processes produce sources of statistical fluctuations and are convolved together, is presented, and a real-world example is given for a scintillation detector. The use of detector data in decision-making is presented using confusion matrices, and the Bayesian viewpoint is explored here. The concept of the Receiver Operating Characteristic (ROC) is introduced. The use of binary classifiers is explored through the application of various machine learning algorithms to the problem of $\mathrm {n}/\gamma$ pulse-shape discrimination.