Bayesian Generalized Linear Models for Correlated Data with Fewer Latent Variables

Oregon Convention Center 

There are many challenges that arise when simulating from Bayesian generalized linear model posterior distributions in practice, especially when the observed data is assumed to be dependent. We focus on two challenges that stem from the introduction of one or more auxiliary latent variables for each observation. First, several popular methods for simulating from Bayesian generalized linear model posterior distributions rely on the introducing of an auxiliary random variable for each observation. These methods can scale poorly when the number of observations is large because they require additional posterior draws and repeated expensive matrix calculations. Second, many of the most useful approaches for introducing dependence in the observed data do so by introducing a latent random variable with a dense but computationally convenient prior covariance matrix. However, the computational conveniences offered by the prior covariance matrix may be absent (or appear to be absent) from the posterior. We introduce methods for addressing these challenges that take advantage of simple reparameterizations of the problem, advances in posterior mode computation, and modern sampling.