Variational Inference for Heteroscedastic Semiparametric Regression

We develop fast mean field variational methodology for Bayesian heteroscedastic semiparametric regression, in which both the mean and variance are smooth, but otherwise arbitrary, functions of the predictors. Our resulting algorithms are purely algebraic, devoid of numerical integration and Monte Carlo sampling. The locality property of mean field variational Bayes implies that the methodology also applies to larger models possessing variance function components. Simulation studies indicate good to excellent accuracy, and considerable time savings compared with Markov chain Monte Carlo. We also provide some illustrations from applications.