SCALABLE BAYESIAN INFERENCE FOR LARGE CROSSED MIXED EFFECTS MODELS

Abstract

Large crossed mixed effects models with imbalanced structures and missing data pose major computational challenges for standard Bayesian posterior sampling algorithms. We propose a class of stochastic gradient MCMC algorithms for such models. Our first contribution is to devise novel algorithms for the crossed mixed effects models for continuous response variables. The first algorithm is developed for the balanced design. The second algorithm, which we call the pigeonhole stochastic gradient Langevin dynamics (PSGLD), is developed for both balanced and unbalanced designs. We provide theoretical guarantees for the proposed algorithms. Our second main contribution is to extend the PSGLD algorithms to generalized crossed mixed effects models with probit and logistic links for binary and categorical data. We incorporate two different data augmentation techniques in PSGLD. A variety of numerical experiments demonstrate that the proposed algorithms can significantly reduce the computational cost and better balance the approximation accuracy and computational efficiency.