  Although multivariate count data are routinely collected in many application
areas, there is surprisingly little work developing flexible models for
characterizing their dependence structure. This is particularly true when
interest focuses on inferring the conditional independence graph. In this
article, we propose a new class of pairwise Markov random field-type models for
the joint distribution of a multivariate count vector. By employing a novel
type of transformation, we avoid restricting to non-negative dependence
structures or inducing other restrictions through truncations. Taking a
Bayesian approach to inference, we choose a Dirichlet process prior for the
distribution of a random effect to induce great flexibility in the
specification. An efficient Markov chain Monte Carlo (MCMC) algorithm is
developed for posterior computation. We prove various theoretical properties,
including posterior consistency, and show that our COunt Nonparametric
Graphical Analysis (CONGA) approach has good performance relative to
competitors in simulation studies. The methods are motivated by an application
to neuron spike count data in mice.
