Reject inference has an established role in the development of scorecards for credit applications. The performance of the rejects, had they been accepted, is inferred to be good or bad in order to obtain a complete picture of the population applying for credit. Once this is done, the scorecard to assess this population can then be developed. But consider the following problem. A company mails its customer base with an offer of additional finance facilities. The problem is: who should it mail to maximize response while minimizing risk, while also minimizing the number of responders who are rejected at application time to avoid jeopardizing the existing customer relationship? This problem has three inferences required to tackle it completely. First there is the classic inference at the point of application to infer which rejects, had they been accepted, would have been good (or bad). Second, there is the inference at the point of mailing to infer which customers, had they been previously mailed, would have responded—a response inference. But third, and most interesting, is the double inference of inferring which of the inferred responders would have subsequently been good, bad, or rejected—an inference on an inference!. This paper discusses the problem and the solution adopted, and gives figures from the analysis (rescaled to protect commercial confidentiality). Marks & Spencer Financial Services cover some of the issues regarding implementation of the Scorex solution within Fair Isaac's Triad, utilizing both CCN and Equifax bureau data – a unique combination of multiple suppliers' products. Further, the results of a mailing campaign are analysed and compared with the predictions.
Copyright (C) 1996, Institute of Mathematics and its Applications
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