Title: Bayesian variable selection for joint mean and covariance models
Authors: Jiaming Shen - The University of Manchester (United Kingdom) [presenting]
Jianxin Pan - The University of Manchester (United Kingdom)
Abstract: Modelling covariance matrices is generally difficult due to two obstacles, i.e., high-dimensionality and positive definiteness. Based on a modified Cholesky decomposition (MCD) of the covariance matrix, we propose to model the mean, the generalised autoregressive parameters and the innovation variances resulting from the MCD, simultaneously, in terms of linear regression models. We consider not only the parameter estimation, but also variable selection through Bayesian analysis. Specifically, Markov chain Monte Carlo (MCMC) sampling strategy is considered and Gibbs sampler is used to draw random samples from the posterior distributions of the model parameters. Bayesian variable selection methods through adding certain shrinkage penalty terms are also investigated. A newly developed R package called BayesJMCM is introduced and its use is demonstrated through both simulated data and real data. A comparison to existing frequency methods is made, showing that more uncertainties from different sources of the models are accounted and more reliable results are obtained.