Robust Bayesian Methods
William M. Bolstad, James Michael Curran · 2016
This chapter explains how statisticians can make Bayesian inference robust against a mis-specified prior by using a mixture prior and marginalizing out the mixture parameter. The chapter shows how one of the main dangers of Bayesian analysis can be avoided. The prior should have relatively high values over the whole range where the likelihood is substantial. The posterior density is between the prior and likelihood, and gives high probability to values that are not supported strongly either by the data or by the prior, which is a very unsatisfactory result. The values given high posterior probability in an example were not supported strongly either by the data or by the prior. The posterior will be in between, and will give high probability to values neither supported by the data or the prior. If there is a conflict between the prior and the data, statisticians should go with the data.