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A Review of Bayesian Statistics and its Application Direction for Nuclear Non-Proliferation
Bayesian statistics, which is an approach to analyzing data based on Bayes’ theorem, is currently widely used in all fields. However, it has been applied very limitedly to studies related to nuclear nonproliferation. Therefore, this paper provides a knowledge base and directions for using various Bayesian techniques in nuclear non-proliferation. First, the concepts and advantages of the Bayesian approach are summarized and the basic solving methods of Bayesian inference are explained. The Bayesian approach enables more precise posterior estimation using the prior probability and the likelihood functions. To solve Bayes’ theorem, it is necessary to use the conjugate prior distribution, which is analytically solvable, or to use a numerical approach with computing power. Next, for several Bayesian statistics methods, the purpose of use and the mathematical derivation process are described. Bayesian linear regression analysis aims for obtaining a function that outputs the closest value to data of variables and results. Factor analysis is mainly used to derive a smaller number of unobserved latent variables that can represent observed variables. The logit and probit model are nonlinear regression models for when the outcome is binary. The hierarchical model is to analyze by introducing hyper-parameters in an integrated manner when there are several groups of similar data. The Bayesian approach of these methods is generally based on the numerical solution of the Bayesian inference of the multivariate normal distribution. Finally, the previous researches that each introduced method have been applied to nuclear non-proliferation are investigated, and research topics that can be applied in the future are suggested. Bayesian statistics have been mainly used for precise estimation of the amount, location, and radioactivity spectrum of nuclear materials using detectors. Using Bayesian approach, it will be possible to perform various analyzes. For example, the change of activeness of nuclear program can be estimated by Bayesian inferences on the frequency and scale of nuclear tests. And it can be tried predicting the production of plutonium according to the core configuration and burnup using the Bayesian linear regression. Also, by introducing the Bayesian approach to factor analysis or logit analysis of nuclear development motives or nuclear proliferation probability, it can be expected to improve precision. With the development of computer technology, the use of Bayesian statistics increases rapidly. Based on the theory and applied topics summarized in this paper, it is expected that Bayesian statistics will be more actively used for nuclear non-proliferation in the future.
