Priors for Random Count Matrices Derived from a Family of Negative Binomial Processes

Understand

We define a family of probability distributions for random count matrices with a potentially unbounded number of rows and columns.

• The three distributions we consider are derived from the gamma-Poisson, gamma-negative binomial, and beta-negative binomial processes.
• Because the models lead to closed-form Gibbs sampling update equations, they are natural candidates for nonparametric Bayesian priors over count matrices.
• A key aspect of our analysis is the recognition that, although the random count matrices within the family are defined by a row-wise construction, their columns can be shown to be i.i.d.