Improving Analytical Understanding Through the Addition of Information: Bayesian and Hybrid Mathematics Approaches

Safety analysts frequently must provide results that are based on sparse (or even no) data. When data (or more data) become available, it is important to utilize the new information optimally in improving the analysis results. Two methods for accomplishing this purpose are Bayesian analysis, where "prior" probability distributions are modified to become "posterior" distributions based on the new data, and hybrid @ossibilistic/probabilistic analysis) where possibilistic "membership" portrays the subjectivity involved and the probabilistic analysis is "frequentist." Each of these approaches has interesting features, and it is advantageous to compare and contrast the two. In addition to describing and contrasting these two approaches, we will discuss how features of each can be combined to give new advantages neither offers by itself.