A bagging-based correction for the mixture model estimator of population size

Area of Science:

• Ecology
• Biostatistics
• Epidemiology

Background:

• Capture-recapture techniques are vital for estimating population sizes across various scientific disciplines.
• Zero-truncated count data, where zero occurrences are not observed, present unique challenges in population estimation.
• The surveillance of diseases like scrapie in Great Britain involves analyzing count data where zero cases are excluded.

Purpose of the Study:

• To address the overestimation of population size caused by the boundary problem in mixture models.
• To propose a refined method for selecting mixture models using the Bayesian Information Criterion (BIC).
• To improve the accuracy of population size estimation in zero-truncated count data scenarios.

Main Methods:

• Utilizing a frequencies of frequencies approach with a zero-truncated count variable.
• Applying discrete mixtures of Poisson distributions to model count data.
• Implementing a bagging procedure combined with the BIC for robust model selection and population size estimation.

Main Results:

• Mixture models, while often providing a good fit, can lead to population size overestimation due to the boundary problem.
• The proposed method, selecting mixture models via BIC and employing a bagging procedure, mitigates this overestimation.
• Using the median of bagged estimates effectively reduces the influence of extreme population size estimates.

Conclusions:

• The refined capture-recapture method demonstrates a remarkable reduction in bias for population size estimation.
• This approach offers a more reliable way to estimate population sizes from zero-truncated count data, as shown in the scrapie surveillance example.
• The combination of BIC model selection and bagging provides a robust strategy for accurate ecological and epidemiological population studies.