I-priors in Bayesian Variable Selection: From Reproducing Kernel Hilbert Spaces to Hamiltonian Monte Carlo

Abstract

I-priors are a class of objective priors for regression functions which makes use of its Fisher information in a function space framework. Currently, I am exploring the use of I-priors in Bayesian variable selection. My talk is a collection of ideas and methods that I picked up along the way in researching my work, in the hopes that it might be of interest and some use in the areas you are working on: 1) Estimation of I-prior models using likelihood methods; 2) The R/iprior package for fitting I-prior models; 3) Shrinkage properties of I-priors and how they link to L2 penalties with individual shrinkage parameters (and equivalently, individual variance hyper-parameters in a Bayesian setting); 4) Estimation of I-prior models in a fully-Bayes setting, with particular interest in the scale parameters; 5) Using Hamiltonian Monte Carlo to obtain better quality MCMC chains for the Bayesian I-prior model. I will also share some information on useful tools and software for reproducible research that I came across during my work, including Shiny apps, GitHub, RStudio (for package development), knitr, and Stan.

Haziq Jamil

Assistant Professor in Statistics

My research interests include statistical theory, methods and computation, with applications towards the social sciences.