Menictas, M. & Wand, M.P. 2015, 'Variational Inference for Heteroscedastic Semiparametric Regression', Australian and New Zealand Journal of Statistics, vol. 57, no. 1, pp. 119-138.View/Download from: UTS OPUS or Publisher's site
© 2015 Australian Statistical Publishing Association Inc. 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.
We derive a variational inference procedure for approximate Bayesian inference in marginal longitudinal semiparametric regression. Fitting and inference is much faster than existing Markov chain Monte Carlo approaches. Numerical studies indicate that the new methodology is very accurate for the class of models under consideration. Copyright 2013 John Wiley & Sons Ltd