Bayesian analysis of one-inflated models for elusive population size estimation

Area of Science:

• Statistics
• Ecology
• Official Statistics

Background:

• Capture-recapture methods are crucial for estimating population sizes, especially for elusive populations.
• One-inflation, where more individuals are captured once than expected, leads to significant overestimation of population size.
• Existing methods often fail to adequately address one-inflation, necessitating new analytical approaches.

Purpose of the Study:

• To propose a novel Bayesian framework for analyzing one-inflated count data.
• To develop methods for accurate population size estimation in the presence of one-inflation.
• To introduce a Bayesian model selection approach for one-inflated distributions.

Main Methods:

• Development of Bayesian models for one-inflated Poisson, geometric, and negative binomial distributions.
• Application of Gibbs sampling for posterior inference of population size.
• Implementation of Bayesian model selection criteria for comparing distributions.

Main Results:

• The proposed Bayesian approach effectively accounts for one-inflation, providing more accurate population size estimates.
• Gibbs sampling efficiently yields posterior distributions for population size.
• The methodology demonstrates robust performance on both simulated and real-world datasets.

Conclusions:

• The Bayesian framework offers a reliable solution for estimating population sizes affected by one-inflation.
• The method has practical implications for fields like ecology and official statistics, as shown by its application to estimating individuals involved in prostitution exploitation.
• Accurate population estimation is vital for informed policy and resource allocation.