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
**R**^{d} 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,
}