Random forests for homogeneous and non-homogeneous Poisson processes with excess zeros

Area of Science:

• Statistics
• Biostatistics
• Machine Learning

Background:

• Poisson processes are common for count data, but often exhibit excess zeros.
• Existing models may struggle with both excess zeros and complex process variations (homogeneous/non-homogeneous).

Purpose of the Study:

• To introduce a novel hurdle methodology for modeling count data with excess zeros.
• To enhance the modeling of homogeneous and non-homogeneous Poisson processes.

Main Methods:

• Utilized a two-forest approach: one for zero probability, one for Poisson parameters.
• Developed specialized splitting criteria for the second forest based on zero-truncated Poisson likelihood.
• Applied the method to homogeneous and non-homogeneous Poisson processes.

Main Results:

• The proposed hurdle methodology effectively models count data with excess zeros.
• Demonstrated superior performance compared to existing methods in simulations.
• Showed robustness in both hurdle (zero-altered) and zero-inflated scenarios.

Conclusions:

• The two-forest hurdle methodology provides a flexible and accurate tool for count data analysis.
• The method is effective for both homogeneous and non-homogeneous Poisson processes with excess zeros.
• Successfully applied to real-world data on elderly healthcare demand.