Demography — the statistical study of human populations — requires projecting births, deaths, and migration decades into the future to inform pension systems, healthcare planning, housing policy, and climate scenarios. Traditional demographic projections used deterministic scenarios (low, medium, high) that provided no probability of occurrence and often failed to capture the actual range of future outcomes. Bayesian methods have revolutionized demographic forecasting by producing genuine probability distributions over future population trajectories.
Bayesian Population Projections
The United Nations Population Division adopted Bayesian methods for its official world population projections beginning with the 2015 revision. The approach, developed by Adrian Raftery and colleagues, models future total fertility rates and life expectancy using Bayesian hierarchical time-series models, then propagates the resulting uncertainty through cohort-component projection models to produce probabilistic population forecasts for every country.
Phase Model Phase I: Pre-transition (high, stable fertility)
Phase II: Fertility transition (decline modeled by double logistic)
Phase III: Post-transition (fluctuation around replacement)
θ_c ~ N(μ_region, Σ_region) [country parameters drawn from regional prior]
The hierarchical structure borrows strength across countries: a nation with limited data benefits from the experience of countries that have undergone similar demographic transitions. The posterior predictive distribution of population size in 2100 captures uncertainty from fertility, mortality, and migration, producing 95% prediction intervals that are far more honest than deterministic scenarios.
Before 2015, the UN published low, medium, and high population variants that were often misinterpreted as equally likely scenarios. The Bayesian approach produces genuine probabilistic projections: the world population in 2100 has an 80% probability interval of roughly 9.6 to 12.4 billion (2024 revision). These probabilistic statements enable risk-based planning that deterministic scenarios cannot support. The methodology uses MCMC to fit hierarchical models to historical demographic data from 200+ countries.
Mortality Estimation and Life Tables
Bayesian methods improve mortality estimation, especially in data-sparse settings. The Lee-Carter model and its Bayesian extensions forecast age-specific mortality rates by decomposing the mortality surface into age patterns and time trends with uncertainty. For developing countries with incomplete vital registration, Bayesian models combine census data, survey data, and sibling survival histories to estimate child and adult mortality rates, with the posterior reflecting the varying quality and coverage of each data source.
Migration Modeling
International migration is the most uncertain component of population projections. Bayesian models estimate migration flows from incomplete and inconsistent data — different countries measure migration differently, and illegal migration is inherently hard to observe. Bayesian harmonization models reconcile conflicting bilateral flow estimates by treating true flows as latent variables and modeling the observation process for each data source.
"Demography is too important to pretend we know the future. Probabilistic population projections tell policymakers not just what might happen, but how confident we should be — and that honesty changes the conversation about planning." — Adrian E. Raftery, University of Washington
Subnational and Small-Area Estimation
Bayesian small-area estimation methods produce demographic estimates for subnational units — counties, districts, census tracts — where direct data are too sparse for reliable estimation. Hierarchical spatial models borrow strength from neighboring areas and similar populations, producing smoothed maps of fertility, mortality, and demographic composition that inform resource allocation and service delivery.
Historical Demography
Bayesian methods reconstruct the demography of past populations from fragmentary records — parish registers, skeletal samples, census fragments. Models for age-at-death estimation from skeletal remains use Bayesian calibration of age indicators, while models for historical fertility and mortality combine multiple imperfect sources in an integrated Bayesian framework, producing population estimates for periods before modern vital registration.