Bayesian Modeling of Nonlinear Poisson Regression with Artificial Neural Networks

TL;DR

This paper introduces a Bayesian neural network-based nonlinear Poisson regression model that improves prediction accuracy for count data over traditional methods, addressing variability in complex datasets.

Contribution

The paper presents a novel Bayesian ANN approach for nonlinear Poisson regression, enhancing modeling flexibility and predictive performance for count data.

Findings

Higher prediction accuracy than traditional models

Effective in modeling complex count data

Validated with simulation and real datasets

Abstract

Being in the era of big data, modeling and prediction of count data have become significantly important in many fields including health, finance, social, etc. Although linear Poisson regression has been widely used to model count and rate data, it might not be always suitable as it cannot capture some inherent variability within complex data. In this study, we introduce a probabilistically driven nonlinear Poisson regression model with Bayesian artificial neural networks (ANN) to model count or 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.