A1696
Title: Scalable Bayesian inference for the generalized linear mixed model
Authors: Sayan Mukherjee - Duke University (United States)
Samuel Berchuck - Duke University (United States) [presenting]
Andrea Agazzi - Universita di Pisa (Italy)
Abstract: The generalized linear mixed model (GLMM) is a popular approach for handling correlated data, and is used extensively in applications where big data is common, including biomedical settings. The focus is scalable statistical inference for the GLMM, where we define statistical inference as: (i) estimation of population parameters, and (ii) evaluation of scientific hypotheses in the presence of uncertainty. Artificial intelligence (AI) learning algorithms excel at scalable statistical estimation, but rarely include uncertainty quantification. In contrast, Bayesian inference provides full statistical inference, since uncertainty quantification results automatically from the posterior distribution. Unfortunately, Bayesian inference algorithms, including Markov Chain Monte Carlo (MCMC), become computationally intractable in big data settings. We introduce a statistical inference algorithm at the intersection of AI and Bayesian inference, that leverages the scalability of modern AI algorithms with guaranteed uncertainty quantification that accompanies Bayesian inference. Our algorithm is an extension of stochastic gradient MCMC with novel contributions that address the treatment of correlated data and proper posterior variance estimation. Through theoretical and empirical results, we establish our algorithm's statistical inference properties and apply the method to a large electronic health records database.
