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Title: Exact Bayesian inference for a class of spatial generalized linear mixed effects models Authors:  Jonathan Bradley - Florida State University (United States) [presenting]
Abstract: Markov chain Monte Carlo (MCMC) has become a standard in Bayesian statistics that allows one to generate dependent replicates from a posterior distribution for general Bayesian hierarchical models. However, convergence issues, tuning, and the effective sample size of the MCMC are nontrivial considerations that are often overlooked or can be difficult to assess. This motivates us to consider finding expressions of the posterior distribution that are computationally straightforward to sample from directly. We focus on a broad class of Bayesian generalized linear mixed-effects models (GLMM) that allows one to jointly model data of different types. We derive a class of distributions that allows one to specify the prior on fixed and random effects to be any conjugate multivariate distribution. The expression of the posterior distribution is given, and direct simulations have an efficient projection form. An analysis of a spatial dataset is presented.