  While there is considerable effort to identify signaling pathways using
linear Gaussian Bayesian networks from data, there is less emphasis of
understanding and quantifying conditional densities and probabilities of nodes
given its parents from the identifed Bayesian network. Most graphical models
for continuous data assume a multivariate Gaussian distribution, which might be
too restrictive. We re-analyse data from an experimental setting considered in
Sachs et al. (2005) to illustrate the effects of such restrictions. For this we
propose a novel non Gaussian nonlinear structural equation model based on vine
copulas. In particular the D-vine regression approach of Kraus and Czado (2017)
is adapted. We show that this model class is more suited to fit the data than
the standard linear structural equation model based on the biological consent
graph given in Sachs et al. (2005). The modelling approach also allows to study
which pathway edges are supported by the data and which can be removed. For
data experiment cd3cd28+aktinhib this approach identified three edges, which
are no longer supported by the data. For each of these edges a plausible
explanation based on underlying the experimental conditions could be found.
