On the Estimation of Homogeneous Population Size in a Complex Dual-record System

TL;DR

This paper addresses the challenge of estimating homogeneous population size in complex dual-record systems with behavioral effects, proposing empirical and full Bayesian methods to improve accuracy and overcome identifiability issues.

Contribution

It introduces two empirical Bayes approaches and a fully Bayesian method for population size estimation in complex DRS models with behavioral effects, supported by extensive simulations and real data analysis.

Findings

Empirical Bayes methods perform well in complex DRS models.

Full Bayesian approach provides robust estimates.

Recommendations depend on knowledge of behavioral response effects.

Abstract

Dual-record system (DRS) (equivalently two sample Capture-recapture experiment) model with time and behavioral response variation, has attracted much attention specifically in the domain of Official Statistics and Epidemiology. The relevant model suffers from parameter identifiability problem and proper Bayesian methodologies could be helpful to overcome the situation. In this article, we have formulated the population size estimation problem in DRS as a missing data analysis under both the known and unknown directional nature of underlying behavioral response effect. Two simple empirical Bayes approaches are proposed and investigated their performances for this complex model along with a fully Bayes treatment. Extensive simulation studies are carried out to compare the performances of these competitive approaches and a real data example is also illustrated. Finally, some features of these methods and recommendations to implement them in practice are explored depending upon the availability of knowledge on the nature of behavioral response effect.