Reconstructing Past Populations With Uncertainty From Fragmentary Data

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.”

Keywords:

• Bayesian hierarchical model
• Cohort component model
• Fertility rate
• International migration
• Markov chain Monte Carlo
• Mortality rate

Acknowledgments

We thank the editor, associate editor, and three anonymous reviewers for very helpful comments. This work was supported by grants R01 HD054511, R01 HD070936, K01 HD057246, and 5R24HD042828 from the Eunice Kennedy Shriver National Institute of Child Health and Human Development (NICHD). The first author received partial support from a Shanahan Endowment Fellowship and NICHD training grant 5T32HD007543 to the Center for Studies in Demography & Ecology, and from the Center for Statistics and the Social Sciences, both at the University of Washington. The views and opinions expressed in this article are those of the authors and do not necessarily represent those of the United Nations. This article has not been formally edited and cleared by the United Nations.