Robust Bayesian regression with the forward search: theory and data analysis

The frequentist forward search yields a flexible and informative form of robust regression. The device of fictitious observations provides a natural way to include prior information in the search. However, this extension is not straightforward, requiring weighted regression. Bayesian versions of forward plots are used to exhibit the presence of multiple outliers in a data set from banking with 1903 observations and nine explanatory variables which shows, in this case, the clear advantages from including prior information in the forward search. Use of observation weights from frequentist robust regression is shown to provide a simple general method for robust Bayesian regression.