Modeling Poisson variables with positive spatial dependence

The Poisson auto-model is a natural vehicle for modeling data that consist of small counts and may exhibit dependence, frequently spatial dependence. Unfortunately, it is not possible to model positive dependence with a regular Poisson auto-model. We develop a model that allows positive dependencies in multivariate count data by specifying conditional distributions as Winsorized Poisson probability mass functions. This model may be used to incorporate either positive or negative dependencies among the variables.