Default estimation and expert information: All likely dataset analysis and robust validation

Default is a rare event, even in segments in the midrange of a bank's portfolio. Inference about default rates is essential for risk management and for compliance with the requirements of Basel II. Most commercial loans are in the middle-risk categories and are to unrated companies. Expert information is crucial in inference about defaults. A Bayesian approach is proposed and illustrated using a prior distribution assessed from an industry expert. The method of All Likely Datasets, based on sufficient statistics and expert information, is used to characterize likely datasets for analysis. A check of robustness is illustrated with an e-mixture of priors.