Nonparametric empirical Bayesian method for noncontractual setting of customer-base analysis

Abstract

In the noncontractual setting of customer-base analysis, heterogeneity parameters in purchase model and lifetime model are usually assumed to follow some familiar parametric distribution such as gamma or log-normal distribution. But, in many applications, these assumptions may be questionable because the true distributions of heterogeneity parameters are usually unknown. To this end, this paper relaxes these assumptions imposed on heterogeneity parameters to develop a nonparametric approach to purchase model and lifetime model, in which unknown distributions of heterogeneity parameters are approximated by a truncated Dirichlet process prior. A nonparametric empirical Bayesian method is developed to obtain Bayesian estimations of unknown parameters in the proposed nonparametric models. The blocked Gibbs sampler is presented to draw observations required for Bayesian inference from the corresponding posterior distributions of the components of parameters. Extensive simulation studies and a CDNOW data set are presented to illustrate the newly developed methodologies.