Bayesian Analysis of Logistic Default Risk Model with Oversampling

Oversampling is a widely applied sampling method in default risk modeling. Although arbitrarily increased portions of the defaulted in sampling makes logistic estimation more efficiently, it will bring biased estimation results at the same time. We present a simple Bayesian analysis method to derive the offset logistic modeling to correct oversampling bias. It is pointed out that the real value of non-defaulted to the defaulted in the offset term is actually unknown. This will bring difficulties in direct testing of validity of the offset model. By some further analysis, we present a novel way to test offset model indirectly. The final empirical evidences convincingly support the offset logistic model we have derived.