Fast Methods for Posterior Inference of Two-Group Normal-Normal Models

We describe a class of algorithms for evaluating posterior moments certain Bayesian linear regression models with normal likelihood and prior on the coefficients. The proposed methods can be used hierarchical mixed effects partial pooling over one group predictors, as well random two groups predictors. demonstrate performance applications, involving U.S. opinion polls modeling COVID-19 outbreaks in Israel using survey data. involve analytical marginalization coefficients followed by numerical integration remaining low-dimensional density. dominant cost is an eigendecomposition computed once each value outside parameter integration. Our approach drastically reduces run times compared to state-of-the-art Markov chain Monte Carlo (MCMC) algorithms. latter, addition being computationally expensive, also difficult tune when applied models.