Non-parametric Bayesian Network for Surrogate Data

In recent years, domain experts indicated increasing interest in Bayesian Networks (BN). BN can be represented by a directed acyclic graph, the nodes of which, corresponding to the random variables under study, are connected by edges representing direct relationship between the nodes. For the unknown distributions of the analyzed variables, non-parametric Bayesian networks (NPBN) are used to build a graphical probabilistic model. The current study focuses on the application of MATLAB toolbox BANSHEE for creating NPBN for a set of surrogate random variables with certain cross-correlation coefficients. An acyclic directed graph was constructed, in which links between parent and child nodes were established based on expert assessment. Gaussian copula based on the Spearman's rank correlation was considered as a metric of interrelation between two connected nodes. Two diagnostic tests were carried out for the constructed NPBN. The Cramer-von Mises test showed that the Gaussian copula represents an effective solution for the characterization of all pairwise interactions between variables. Calculation of the d- calibration score confirmed that the Gaussian copula matches the proposed BN structure.