A1321
Title: Exact MCMC-free Bayesian inference for data of any size
Authors: Jonathan Bradley - Florida State University (United States) [presenting]
Abstract: Fine particulate matter and aerosol optical thickness are two variables of interest to scientists for understanding air quality and its various health and ecological impacts. Data on these variables are extremely large, making Bayesian analysis impractical. Scalable exact posterior regression (S-EPR) is introduced, which combines two recently introduced methodologies: the data subset approach and exact posterior regression (EPR). The "data subset approach" assumes a parametric model for a low-dimensional training dataset and assumes the remaining holdout data follows its true data-generating mechanism. Posterior samples from this model scale to the low-dimensional training data while simultaneously including all the available data, making Bayesian inference from this model scalable to arbitrary dimensions. The data subset approach is combined with a Bayesian hierarchical model that allows one to sample independent replicates of fixed and random effects directly from the posterior without the use of MCMC or approximations. Samples from the posterior distribution have an efficient projection form and, hence, are referred to as EPR. For the first time, an exact, fully Bayesian method for a class of spatial GLMMs can be scaled to arbitrary dimensions and does not require MCMC. The benefits of S-EPR are illustrated via the motivating application.
