A Bayesian Framework for Single-Sample Population Size Estimation Using Parent-Offspring Data

Estimating the size of a finite population from a single sampling occasion remains a critical challenge across diverse disciplines due to the logistical and financial limitations of traditional methods. While Close-Kin Mark-Recapture (CKMR) has recently offered a molecular genetics solution in statistical ecology, this paper demonstrates that the underlying mathematical principles can be generalized to any system where sampled individuals can be linked through parent-offspring relationships . We propose an original Bayesian framework that approaches the inference problem from a novel data-generation perspective, providing both condizional and complete data likelohood solution. We derive a non-informative Jeffreys prior for the model parameters, proving that the resulting posterior distribution is proper under mild, easily met logical constraints. The flexibility and generality of this framework is demonstrated beyong ecological application. We successfully apply the model to a criminal network dataset derived from Italian judicial acts "Operazione Infinito". Here, "parents" are interpreted as clan bosses and "offspring" as affiliates, showcasing how the framework can accurately infer hidden population structures based purely on relational connectivity.