As Japan's population ages, the shifting age distribution threatens to destabilize economic and social conditions. Exacerbating this issue is increasing urbanization that leaves vulnerable demographics isolated in more rural regions. To make meaningful statements about the future of Japan's demographic distribution, it is necessary to analyze population movement within the country. To this end, we perform a descriptive analysis examining the net immigration rates into each prefecture of Japan from other prefectures over the course of 2004 to 2013. In particular, we propose a Bayesian regression model of net immigration rates which incorporates eects of census variables, latent differences between prefectures, and anomalous shocks in wake of the 2011 Tohoku earthquake and subsequent nuclear meltdown. We use two-component spike-and-slab priors on regression coefficients that allow for selective shrinkage of parameters. We further propose a framework for predicting from the model and demonstrate that it provides accurate predictions even for years for which covariate values are not known. Our model is seen to give robust predictions of immigration rates, while also yielding valuable insights about the potential factors influencing migration between regions of Japan.