We produce probabilistic projections of population for all countries based on probabilistic projections of fertility, mortality, and migration. We compare our projections to those from the United Nations' Probabilistic Population Projections, which uses similar methods for fertility and mortality but deterministic migration projections. We find that uncertainty in migration projection is a substantial contributor to uncertainty in population projections for many countries. Prediction intervals for the populations of Northern America and Europe are over 70% wider, whereas prediction intervals for the populations of Africa, Asia, and the world as a whole are nearly unchanged. Out-of-sample validation shows that the model is reasonably well calibrated.Bayesian hierarchical model | international migration | predictive distribution | United Nations | World Population Prospects I n this paper we describe a method for probabilistic projection of population for all countries, with a focus on accounting for uncertainty in projections of international migration. In particular, we are motivated by the needs of the United Nations (UN) Population Division in producing population projections for all countries until 2100 based on projections of fertility, mortality, and migration.A variety of forces contribute to the ebb and flow of international migration. Economic theories at varying levels of granularity indicate that migration flows can arise from individual attempts to maximize income (1, 2), household-level mitigation of risk (3, 4), or differences in global supply and demand for labor (5, 6). Individuals decide to migrate based on an assessment of push and pull factors (7), which may include migration policy (8), geopolitical conflict (9), and quality of the natural environment (10, 11). Networks of migrants provide a feedback mechanism such that migration flows tend to perpetuate themselves over time (12,13). Bijak (14) gives a thorough overview of theories and models of international migration. Despite their acknowledged role in driving migration, our model does not make use of push and pull factors, economic or otherwise, as covariates. Such factors are largely too difficult to predict in the long term to be of use. Instead, we appeal to the inertia of selfperpetuating migration patterns by modeling migration as an autoregressive process.Historically, most methods for projecting population have been deterministic. If the current population is known, broken down by age and sex, and future age-and sex-specific rates are projected for fertility, mortality, and migration, then the cohortcomponent method produces population projections (15). However, the UN Population Division now produces probabilistic projections of population, fertility, and mortality for all countries, but these projections still condition on deterministic migration projections (16, 17). The current methodology in the UN's World Population Prospects (WPP) differs from country to country but typically projects that net migration counts will remain cons...