Bayesian modelling of nonlinear Poisson regression with artificial neural networks

Modelling and prediction of count and rate responses have substantial usage in many fields, including health, finance, social, etc. Conventionally, linear Poisson regression models have been widely used to model these responses. However, the linearity assumption of the systematic component of linear Poisson regression models restricts their capability of handling complex data patterns. In this regard, it is important to develop nonlinear Poisson regression models to capture the inherent variability within the count data. In this study, we introduce a probabilistically driven nonlinear Poisson regression model with Bayesian artificial neural networks (ANN) to model count and rate data. This new nonlinear Poisson regression model developed with Bayesian ANN provides higher prediction accuracies over traditional Poisson or negative binomial regression models as revealed in our simulation and real data studies.