Lots of studies are based on simulating count data from a Poisson distribution. Many simulate multiple Poisson variables that should be correlated, but are simplistically generated as independent. Our just-published paper "On Generating Multivariate Poisson Data in Management Science Applications" co-authored with Inbal Yahav introduces a practical method for simulating correlated multivariate Poisson count data -- highly useful in many applications! Here's the abstract (full paper here)

Generating multivariate Poisson random variables is essential in many applications, such as multi echelon supply chain systems, multi-item/multi-period pricing models, accident monitoring systems, etc. Current simulation methods suffer from limitations ranging from computational complexity to restrictions on the structure of the correlation matrix, and therefore are rarely used in management science. Instead, multivariate Poisson data are commonly approximated by either univariate Poisson or multivariate Normal data. However, these approximations are often not adequate in practice. In this paper, we propose a conceptually appealing correction for NORTA (NORmal To Anything) for generating multivariate Poisson data with a flexible correlation structure and rates. NORTA is based on simulating data from a multivariate Normal distribution and converting it into an arbitrary continuous distribution with a specific correlation matrix.We show that our method is both highly accurate and computationally efficient. We also show the managerial advantages of generating multivariate Poisson data over univariate Poisson or multivariate Normal data.