Year
2015
Degree Name
Doctor of Philosophy
Department
School of Mathematics and Applied Statistics
Recommended Citation
Wang, Shen, Variational inference machines for semiparametric regression, Doctor of Philosophy thesis, School of Mathematics and Applied Statistics, University of Wollongong, 2015. https://ro.uow.edu.au/theses/4666
Abstract
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.
FoR codes (2008)
0104 STATISTICS, 010401 Applied Statistics, 010405 Statistical Theory
Unless otherwise indicated, the views expressed in this thesis are those of the author and do not necessarily represent the views of the University of Wollongong.