Bayesian Adaptive Selection Under Prior Ignorance

Abstract

Bayesian variable selection is one of the popular topics in modern day statistics. It is an important tool for high dimensional statistics, where the number of model parameters is greater than the number of observations. Several Bayesian models have been proposed for variable selection. However, a convincing robust Bayesian approach is yet to be investigated. Here in this work, we investigate sensitivity analysis over a simplex of probability measures. We sample from this simplex to get an inclusion probability of each variable. The sensitivity analysis gives us a set of posteriors instead of a single posterior. This set of posteriors gives us a behaviour of the model parameters with respect to different prior elicitations resulting in robust inferential conclusions.