Minimum message length inference with application to genome-wide association studies data

© 2019 Dr. Chi Kuen WongMinimum Message Length (MML) is a Bayesian framework for model selection and statistical inference with a strong foundation in information theory. This thesis examines the MML criterion for model selection by applying MML to important model selection problems. The first major contribution addresses the application of MML to a small-sample model selection problem involving Poisson and geometric models. Since MML is a Bayesian principle, it requires prior distributions for all model parameters. We introduce three candidate prior distributions for the model parameters with both light and heavy-tails. The performance of our proposed MML methods are compared with objective Bayesian inference and minimum description length techniques through simulations. We found that using a heavy-tail prior distribution leads to good model selection results for the MML criterion. The second major contribution investigates the application of MML to Student-t linear regression, which allows a more robust modelling than the Gaussian linear regression. We propose a novel criterion for model selection in Student-t linear regression based on MML. We derive a suitable non-informative proper uniform prior distribution for the regression coefficients that leads to a simple and easy-to-apply criterion. Our proposed criterion is free of user specified hyperparameters and is invariant under both full rank transformations of the design matrix and linear transformations of the outcome. Furthermore, we demonstrate a practical application of this work by applying the MML criterion to a genome-wide association studies (GWAS) data on maize