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.

Date
Location
LSE, London, United Kingdom