Identifying future defaulters: A hierarchical Bayesian method

• We develop a hierarchical mixture cure model for credit scoring.
• We relax the independence assumption of the probability and the time of default.
• Empirical study shows that the customers with higher risk may default later and thus contribute a higher profit.
• Traditional classification methods should be carefully applied to the censored data.
• Our model is successful in identifying future defaulters even when default occurs much later than the censoring date.

Traditional methods of applying classification models into the area of credit scoring may ignore the effect from censoring. Survival analysis has been introduced with its ability to deal with censored data. The mixture cure model, one important branch of survival models, is also applied in the context of credit scoring, assuming that the study population is a mixture of never-default and will-default customers.We extend the standard mixture cure model through: (1) relaxing the independence assumption of the probability and the time of default; (2) treating the missing defaulting labels as latent variables and applying an augmentation technique; and (3) introducing a discrete truncated exponential distribution to model the time of default. Our full model is written in a hierarchical form so that the Markov chain Monte Carlo method is applied to estimate corresponding parameters.Through an empirical analysis, we show that both mixture models, the standard mixture cure model and the hierarchical mixture cure model (HMCM), are more advanced in identifying future defaulters while compared with logistic regression. It is also concluded that our hierarchical Bayesian extension increases the model’s predictability and provides meaningful output for risk management.