Visualizing Conditional Dependencies in Hyper-Graph Models

A parameterization of hypergraphs based on the geometry of points in $rr^m$ is developed. Given this parameterization, informative priors on hypergraphs are induced by priors on point configurations via spatial processes. This prior specification is used to infer conditional independence models or Markov structure of a multivariate distribution. Specifically, we can recover both the factorization as well as the hyper Markov law. The advantages of this approach are greater control on the distribution of graph features than Erd"{o}s-R'{e}nyi random graphs, inference of factorizations that cannot be retreived by a graph alone, and Markov chain Monte Carlo algorithms that allow for local and global moves in graph space. We illustrate the utility of this parameterization and prior specification using simulations.