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Reconstructing Past Populations With Uncertainty From Fragmentary Data

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  • Mark C. Wheldon
  • Adrian E. Raftery
  • Samuel J. Clark
  • Patrick Gerland

Abstract

Current methods for reconstructing human populations of the past by age and sex are deterministic or do not formally account for measurement error. We propose a method for simultaneously estimating age-specific population counts, fertility rates, mortality rates, and net international migration flows from fragmentary data that incorporates measurement error. Inference is based on joint posterior probability distributions that yield fully probabilistic interval estimates. It is designed for the kind of data commonly collected in modern demographic surveys and censuses. Population dynamics over the period of reconstruction are modeled by embedding formal demographic accounting relationships in a Bayesian hierarchical model. Informative priors are specified for vital rates, migration rates, population counts at baseline, and their respective measurement error variances. We investigate calibration of central posterior marginal probability intervals by simulation and demonstrate the method by reconstructing the female population of Burkina Faso from 1960 to 2005. Supplementary materials for this article are available online and the method is implemented in the R package "popReconstruct."

Suggested Citation

  • Mark C. Wheldon & Adrian E. Raftery & Samuel J. Clark & Patrick Gerland, 2013. "Reconstructing Past Populations With Uncertainty From Fragmentary Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(501), pages 96-110, March.
    • Handle: RePEc:taf:jnlasa:v:108:y:2013:i:501:p:96-110
    DOI: 10.1080/01621459.2012.737729
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    Cited by:

    1. Miikka Voutilainen & Jouni Helske & Harri Högmander, 2020. "A Bayesian Reconstruction of a Historical Population in Finland, 1647–1850," Demography, Springer;Population Association of America (PAA), vol. 57(3), pages 1171-1192, June.
    2. Arkadiusz Wiśniowski & Peter Smith & Jakub Bijak & James Raymer & Jonathan Forster, 2015. "Bayesian Population Forecasting: Extending the Lee-Carter Method," Demography, Springer;Population Association of America (PAA), vol. 52(3), pages 1035-1059, June.
    3. Wazir Asif & Goujon Anne, 2021. "Exploratory Assessment of the Census of Pakistan Using Demographic Analysis," Journal of Official Statistics, Sciendo, vol. 37(3), pages 719-750, September.
    4. David J Sharrow & Samuel J Clark & Adrian E Raftery, 2014. "Modeling Age-Specific Mortality for Countries with Generalized HIV Epidemics," PLOS ONE, Public Library of Science, vol. 9(5), pages 1-10, May.
    5. Yigang Wei & Zhichao Wang & Huiwen Wang & Yan Li & Zhenyu Jiang, 2019. "Predicting population age structures of China, India, and Vietnam by 2030 based on compositional data," PLOS ONE, Public Library of Science, vol. 14(4), pages 1-42, April.
    6. Arkadiusz Wiśniowski, 2017. "Combining Labour Force Survey data to estimate migration flows: the case of migration from Poland to the UK," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(1), pages 185-202, January.

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