  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.
