A flexible multivariate model for high-dimensional correlated count data

We propose a flexible multivariate stochastic model for over-dispersed count data. Our methodology is built upon mixed Poisson random vectors ( Y 1 ,…, Y d ), where the { Y i } are conditionally independent Poisson random variables. The stochastic rates of the { Y i } are multivariate distributions with arbitrary non-negative margins linked by a copula function. We present basic properties of these mixed Poisson multivariate distributions and provide several examples. A particular case with geometric and negative binomial marginal distributions is studied in detail. We illustrate an application of our model by conducting a high-dimensional simulation motivated by RNA-sequencing data.