Extending graphical models for applications: on covariates, missingness and normality

The authors of the paper “Bayesian Graphical Models for Modern Biological Applications” have put forward an important framework for making graphical models more useful in applied settings. In this discussion paper, we give a number of suggestions for making this framework even more suitable for practical scenarios. Firstly, we show that an alternative and simplified definition of covariate might make the framework more manageable in high-dimensional settings. Secondly, we point out that the inclusion of missing variables is important for practical data analysis. Finally, we comment on the effect that the Gaussianity assumption has in identifying the underlying conditional independence graph and how this can be circumvented. The Bayesian framework proposed by the authors is flexible enough to accommodate extensions that can deal with these aspects, which are often encountered in real data analyses such as the complex modern applications considered by the authors.