Gaussian-related undirected graphical models for circular variables

Graphical models are pivotal in studying the conditional independence structure of a set of random variables. Circular variables, arising in several contexts and fields, are characterized by periodicity. Models for studying the dependence/independence structure of circular variables are under-explored but of increasing interest. This paper delves into two multivariate circular distributions, the Wrapped Normal and the Inverse Stereographic Normal distribution as undirected graphical models. For each of these distributions, we study their key properties with respect to conditional independence and introduce specific classes of graphical models. The usefulness of the proposal is shown by modelling the conditional independence among dihedral angles that play a critical role in defining the three-dimensional structure and functionality of proteins. This can provide valuable insights, for instance, into the multiform protein folding understanding.