Variational inference machines for semiparametric regression

Variational approximation methods are enjoying an increasing amount of development and use in statistical problems. In the Bayesian field, we develop mean field variational Bayes (MFVB) algorithms that perform variable selection and fit complicated regression models. We also produce a new Bayesian inference software, InferMachine(), which can perform the MFVB inference using BRugs model code. Finally, a new computational framework, Infer.NET, for approximate Bayesian inference in hierarchical Bayesian models is demonstrated. We assess the accuracy of MFVB via comparison with a Markov chain Monte Carlo (MCMC) baseline. The simulation results show that the results of the MFVB inference agree with those of the MCMC approach. In the non-Bayesian field, the precise asymptotic distributional behaviour of Gaussian variational approximate estimators in a single predictor Poisson mixed model is derived. A simulation study shows that the Gaussian variational approximate confidence intervals possess good to excellent coverage properties.