The prior PDF of generalized data is defined by prior expectation values and a prior covariance matrix of generalized data that naturally includes covariance between any two components of generalized data. | Bayesian optimization of generalized data EPJ Nuclear Sci. Technol. 4 30 2018 Nuclear Sciences G. Arbanas et al. published by EDP Sciences 2018 amp Technologies https epjn 2018038 Available online at https REGULAR ARTICLE Bayesian optimization of generalized data Goran Arbanas1 Jinghua Feng1 2 Zia J. Clifton1 3 Andrew M. Holcomb1 Marco T. Pigni1 Dorothea Wiarda1 Christopher W. Chapman1 4 Vladimir Sobes1 Li Emily Liu2 and Yaron Danon2 1 Nuclear Data and Criticality Safety Group Reactor and Nuclear Systems Division Oak Ridge National Laboratory Oak Ridge TN 37831-6171 USA 2 Department of Mechanical Aerospace and Nuclear Engineering Rensselaer Polytechnic Institute Troy NY 12180-3590 USA 3 Department of Physics and Astronomy University of Alabama Huntsville AL 35899 USA 4 Nuclear amp Radiological Engineering amp Medical Physics Georgia Institute of Technology Atlanta GA 30332-0745 USA Received 31 October 2017 Received in final form 11 April 2018 Accepted 28 May 2018 Abstract. Direct application of Bayes theorem to generalized data yields a posterior probability distribution function PDF that is a product of a prior PDF of generalized data and a likelihood function where generalized data consists of model parameters measured data and model defect data. The prior PDF of generalized data is defined by prior expectation values and a prior covariance matrix of generalized data that naturally includes covariance between any two components of generalized data. A set of constraints imposed on the posterior expectation values and covariances of generalized data via a given model is formally solved by the method of Lagrange multipliers. Posterior expectation values of the constraints and their covariance matrix are conventionally set to zero leading to a likelihood function that is a Dirac delta function of the constraining equation. It is shown that setting constraints to values other than zero is analogous to introducing a model defect. Since .
