Current methods for reconstructing human populations of the past by age and sex are deterministic or do not formally account for measurement error. I propose \"Bayesian reconsruction\", 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. Expert opinion is incorportated formally through informative priors. Inference is based on joint posterior probability distributions which yield fully probabilistic interval estimates. Previous methods of reconstruction did not account for measurement error, or imposed fixed age-patterns on some parameters. 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. Statistical properties of Bayesian reconstruction are investigated through simulation and sensitivity analyzes. The method is applied to real data from Burkina Faso, Laos, New Zealand, Sri Lanka, Thailand and India, demonstrating its applicability to developing and developed countries.
It can also be used to compare model life tables. When full populations are reconstructed, probabilistic estimates of sex ratios, such as the sex ratio at birth and sex ratios of mortality, can also be obtained. Bayesian reconstruction is implemented in the R package popReconstruct.