Advisor: Adrian Raftery The future of international migration is a topic of great social and political importance, and yet international migration is hard to even estimate, let alone predict. The unreliability of point projections of migration indicates a need for better quantification of uncertainty in migration projections. We accomplish this quantification of uncertainty with a Bayesian hierarchical autoregressive model on net migration rates. In an initial model, we assume error terms are independent across countries. A natural extension is to allow between-country correlations of errors. However, with many countries and few time points, these correlations are hard to estimate. We provide a method for regularized correlation matrix estimation which incorporates informative prior information. Our method allows beliefs about correlations to be expressed as Laplace priors on the elements of the correlation matrix, producing in the end a maximum a posteriori correlation estimate.