Geometric Representations of Hypergraphs for Prior Specification and Posterior Sampling

Geometric Representations of Hypergraphs
for Prior Specification and Posterior Sampling

Simón Lunagómez, Sayan Mukherjee, Robert L. Wolpert

Duke University

Feb 2009 (Revised: Dec 2009)

A parametrization of hypergraphs based on the geometry of points in Rd is developed. Informative prior distributions on hypergraphs are induced through this parametrization by priors on point configurations via spatial processes. This prior specification is used to infer conditional independence models or Markov structure of multivariate distributions. Specifically, we can recover both the junction tree factorization as well as the hyper Markov law. This approach offers greater control on the distribution of graph features than Erdös-Rényi random graphs, supports inference of factorizations that cannot be retrieved by a graph alone, and leads to new Metropolis/Hastings Markov chain Monte Carlo algorithms with both local and global moves in graph space. We illustrate the utility of this parametrization and prior specification using simulations.

Keywords: Computational topology, Factor models, Geometric random graphs, Graphical models, Simplicial complex.


The manuscript is available PDF format (1.7mb).


Cite as:

@TechReport{Luna:Mukh:Wolp:2009,
      Author = "Sim{\'o}n Lunag{\'o}mez and Sayan Mukherjee and
                Robert L. Wolpert", 
       Title = "Geometric Representations of Hypergraphs for Prior
                Specification and Posterior Sampling",
 Institution = "Duke University Department of Statistical Science",
        Type = "Discussion Paper",
      Number = "2009-01",
         URL = "http://ftp.stat.duke.edu/WorkingPapers/09-01.html",
        Year = 2009,
}