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Bayesian population size estimation using Dirichlet process mixtures

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  • Daniel Manrique‐Vallier

Abstract

We introduce a new Bayesian nonparametric method for estimating the size of a closed population from multiple‐recapture data. Our method, based on Dirichlet process mixtures, can accommodate complex patterns of heterogeneity of capture, and can transparently modulate its complexity without a separate model selection step. Additionally, it can handle the massively sparse contingency tables generated by large number of recaptures with moderate sample sizes. We develop an efficient and scalable MCMC algorithm for estimation. We apply our method to simulated data, and to two examples from the literature of estimation of casualties in armed conflicts.

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  • Daniel Manrique‐Vallier, 2016. "Bayesian population size estimation using Dirichlet process mixtures," Biometrics, The International Biometric Society, vol. 72(4), pages 1246-1254, December.
    • Handle: RePEc:bla:biomet:v:72:y:2016:i:4:p:1246-1254
    DOI: 10.1111/biom.12502
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    References listed on IDEAS

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    1. S. E. Fienberg & M. S. Johnson & B. W. Junker, 1999. "Classical multilevel and Bayesian approaches to population size estimation using multiple lists," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 162(3), pages 383-405.
    2. Yajuan Si & Jerome P. Reiter, 2013. "Nonparametric Bayesian Multiple Imputation for Incomplete Categorical Variables in Large-Scale Assessment Surveys," Journal of Educational and Behavioral Statistics, , vol. 38(5), pages 499-521, October.
    3. Dunson, David B. & Xing, Chuanhua, 2009. "Nonparametric Bayes Modeling of Multivariate Categorical Data," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 1042-1051.
    4. William A. Link, 2003. "Nonidentifiability of Population Size from Capture-Recapture Data with Heterogeneous Detection Probabilities," Biometrics, The International Biometric Society, vol. 59(4), pages 1123-1130, December.
    5. Shira Mitchell & Al Ozonoff & Alan M. Zaslavsky & Bethany Hedt-Gauthier & Kristian Lum & Brent A. Coull, 2013. "A Comparison of Marginal and Conditional Models for Capture–Recapture Data with Application to Human Rights Violations Data," Biometrics, The International Biometric Society, vol. 69(4), pages 1022-1032, December.
    6. Fodé Tounkara & Louis‐Paul Rivest, 2015. "Mixture regression models for closed population capture–recapture data," Biometrics, The International Biometric Society, vol. 71(3), pages 721-730, September.
    7. Baillargeon, Sophie & Rivest, Louis-Paul, 2007. "Rcapture: Loglinear Models for Capture-Recapture in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 19(i05).
    8. Stephen Fienberg & Daniel Manrique-Vallier, 2009. "Integrated methodology for multiple systems estimation and record linkage using a missing data formulation," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 93(1), pages 49-60, March.
    9. Richard Arnold & Yu Hayakawa & Paul Yip, 2010. "Capture–Recapture Estimation Using Finite Mixtures of Arbitrary Dimension," Biometrics, The International Biometric Society, vol. 66(2), pages 644-655, June.
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    1. Daniel Manrique‐Vallier & Jingchen Hu, 2018. "Bayesian non‐parametric generation of fully synthetic multivariate categorical data in the presence of structural zeros," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 181(3), pages 635-647, June.

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