The one-inflated positive Poisson mixture model for use in population size estimation

Area of Science:

• Ecology
• Statistics
• Population Dynamics

Background:

• Capture-recapture methods are crucial for estimating population sizes.
• Standard models may struggle with specific data characteristics like one-inflation and unobserved heterogeneity.
• Existing estimators can exhibit bias or fail when these features are present.

Purpose of the Study:

• To introduce the one-inflated positive Poisson mixture model (OIPPMM).
• To utilize OIPPMM as a truncated count model within Horvitz-Thompson estimation.
• To address limitations of current methods in capture-recapture analyses.

Main Methods:

• Development of the one-inflated positive Poisson mixture model (OIPPMM).
• Application of OIPPMM within the Horvitz-Thompson estimation framework.
• Comparison of OIPPMM with existing population estimation techniques.

Main Results:

• The OIPPMM effectively handles one-inflation and unobserved heterogeneity in capture-recapture data.
• OIPPMM yields significantly different results compared to other popular estimators.
• The proposed model resolves the boundary problem inherent in some estimation methods.

Conclusions:

• The OIPPMM is a robust and effective tool for estimating unknown population sizes.
• This model offers a superior alternative to existing estimators when dealing with one-inflated and heterogeneous data.
• OIPPMM provides a novel solution to the boundary problem in population estimation.