An Introduction to Bayesian Statistics with an Application in Safeguards

Bayesian statistics is a form of statistical inference. Bayesian statisticians believe that information about process or population characteristics, prior to observing any data, can be adequately described with a probability distribution called a prior. This prior distribution, combined with observed data from the process or population of interest, is then updated to what is known as the posterior distribution. The posterior distribution is the primary device used for inference in Bayesian statistics. The purpose of this paper is to give a brief introduction to Bayesian philosophy and concepts. These concepts will then be illustrated with an example from safeguards. An outline of the material is as follows: Section 1 briefly discusses two types of probability and their relation to the two schools of thought in statistics. Section 2 uses conditional probabilities to derive Bayes’ Rule. Section 3 discusses the prior and posterior distributions. Finally, Section 4 presents a simple exercise to illustrate the type of inferences valid under a Bayesian paradigm.