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A cautionary note on Bayesian estimation of population size by removal sampling with diffuse priors
Author(s) -
Bord Séverine,
Bioche Christèle,
Druilhet Pierre
Publication year - 2018
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.201700060
Subject(s) - prior probability , hyperparameter , estimator , sampling (signal processing) , statistics , bayes' theorem , population , bayesian probability , mathematics , population size , econometrics , sample size determination , computer science , algorithm , demography , filter (signal processing) , sociology , computer vision
We consider the problem of estimating a population size by removal sampling when the sampling rate is unknown. Bayesian methods are now widespread and allow to include prior knowledge in the analysis. However, we show that Bayes estimates based on default improper priors lead to improper posteriors or infinite estimates. Similarly, weakly informative priors give unstable estimators that are sensitive to the choice of hyperparameters. By examining the likelihood, we show that population size estimates can be stabilized by penalizing small values of the sampling rate or large value of the population size. Based on theoretical results and simulation studies, we propose some recommendations on the choice of the prior. Then, we applied our results to real datasets.