The pair-copula Bayesian network (PCBN) is a Bayesian network (BN) where the conditional probability functions are modeled using pair-copula constructions. By assigning bivariate conditional copulas to the arcs of the BN, one finds a proper joint density which can flexibly model all kinds of dependence structures. It is a known problem that the PCBN may require numerical integration to perform computations such as sampling and likelihood-inference. To address this issue we propose novel restrictions on the graphical structure and assignment of copulas such that integration will not be required. The resulting restricted PCBN offers significant computational benefits. We establish how to estimate and conduct a structure search for the restricted PCBN. A simulation study shows that a restricted PCBN is able to model non-Gaussian dependence structures more accurately than the widely used Gaussian Bayesian network.

This study discusses the filtration of micro-pollutants and natural organic matter
from water by a granular activated carbon filter. To determine the efficiency of a
filter, simulations are run to predict it’s efficiency. This study will describe a demo application and it’s underlying model that are used to determine the efficiency of a filter over time. The model is able to predict the adsorption of pollutants by the filter. But the model requires a high computational power. A solution to this problem is to look for a better time-integration method. This study will look into the filtration process and usage of time integration-methods on the model. The following research question will be posed: What numerical method is most valid for the simulation of the filtration process by a GAC filter?