Assessing and improving model fitness in MOCABA data assimilation

A mathematical and computational framework is introduced to assess and improve the fitness of multivariate distribution models used in combination with the Bayesian data assimilation framework MOCABA. This is achieved by expanding the distribution model using invertible vairable transformations. Such model expansions enable us to generalize the basic MOCABA framework in order to make it applicable also to observables whose uncertainty distributions significantly deviate from normal distributions. Comparing inferences made on the basis of a normal distribution model with inferences made on the basis of a generalized model enables us to assess the fitness of the normal distribution model. Moreover, in cases where the normal distribution model performs poorly, we may switch to a generalized model with a better performance and assess its fitness by comparing its inferences to inferences from other generalized models. The presented methodology can be used for non-perturbative Bayesian updating of basic input parameters (e.g. nuclear data) or, more generally, of integral functions of these parameters (e.g. the power distribution in a nuclear reactor). In this paper, we focus on generalized distribution models based on variable transformations related to the Johnson $S_U$ distribution. To give an illustration of the generalized MOCABA method and to demonstrate its practical benefit, we apply it to the criticality safety analysis of a spent fuel pool for PWR fuel assemblies using data from a large number of different criticality safety benchmark experiments.