Bayesian modelling of nonlinear Poisson regression with artificial neural networks

Area of Science:

• Statistics
• Machine Learning
• Data Science

Background:

• Count and rate data are prevalent across health, finance, and social sciences.
• Linear Poisson regression models are conventionally used but limited by linearity assumptions for complex patterns.
• There is a need for nonlinear models to capture inherent variability in count data.

Purpose of the Study:

• To introduce a probabilistically driven nonlinear Poisson regression model.
• To leverage Bayesian artificial neural networks (ANN) for modeling count and rate data.
• To enhance prediction accuracy for complex count data patterns.

Main Methods:

• Development of a nonlinear Poisson regression model.
• Integration of Bayesian artificial neural networks (ANN) within the Poisson framework.
• Validation through simulation studies and real-world data analysis.

Main Results:

• The proposed Bayesian ANN-based nonlinear Poisson model achieves higher prediction accuracies.
• Outperforms traditional Poisson and negative binomial regression models.
• Effectively captures complex patterns in count and rate data.

Conclusions:

• The Bayesian ANN nonlinear Poisson regression model offers a powerful alternative for count and rate data analysis.
• Provides improved predictive performance over conventional linear models.
• Suitable for applications requiring accurate modeling of count and rate responses.