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Title: Fast and scalable posterior simulation for Gaussian hierarchical models with ICAR spatial random effects Authors:  Marco Ferreira - Virginia Tech (United States) [presenting]
Abstract: A novel algorithm is developed for the simulation from the posterior distribution of Gaussian hierarchical models with intrinsic conditional autoregressive (ICAR) spatial random effects. ICAR specifications assume a neighborhood structure that implies a sparse precision matrix for the spatial random effects. The algorithm is based on the spectral decomposition of the spatial random effects precision matrix. The algorithm is a Markov chain Monte Carlo algorithm that scales linearly with the size of the sample size. We perform a simulation study that shows improved performance of our algorithm when compared to competing existing posterior simulators. Finally, we illustrate the application of our novel algorithm with a spatial regression study of median household income in the contiguous United States in 2017 per county.