Bayesian Decisive Prediction of the Future Optimal Cut-Off Score in Direct Marketing Using BLINEX Loss

• Activity Number: 374
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Martin Levy*+ and Vijay Chakilam and Daling Wen
• Companies: University of Cincinnati and and Genworth
• Keywords: Bayesian Decision Theory ; Predictive Inference ; BLINEX loss ; Scoring models

Abstract

Direct marketing starts with name list. A scoring model creates activation scores from attributes in the name list that are ranked in descending order of activation likelihood. Names of good prospects must be selected via a cutoff. Selecting too many names results in more revenues but perhaps less profit, i.e., profits diminish when costs outweigh gains from activation among bad prospects. The decision problem is: predict an optimal mailing size in a future mailing to maximize profit. The loss function is asymmetric BLINEX (failure to choose good prospects carries a higher penalty than including too many bad prospects) with two parameters. The data should be optimal scores from past direct mail campaigns. We illustrate using a bootstrapping-like strategy to generate "historical" trials. The likelihood function of the optimal activation scores is normal-gamma with unknown mean and variance. Bayesian decisive prediction is applied using conjugate priors with four hyperparameters obtained by the ML-II method. Fractional factorial analysis and half-normal plotting show that of the six parameters, the BLINEX asymmetry and scale parameters, and prior mean are most influential factors.