Nonparametric Hierarchal Bayesian Modeling in Non-contractual Heterogeneous Survival Data

An important problem in the non-contractual marketing domain is discovering the customer lifetime and assessing the impact of customer's characteristic variables on the lifetime. Unfortunately, the conventional hierarchical Bayes model cannot discern the impact of customer's characteristic variables for each customer. To overcome this problem, we present a new survival model using a non-parametric Bayes paradigm with MCMC. The assumption of a conventional model, logarithm of purchase rate and dropout rate with linear regression, is extended to include our assumption of the Dirichlet Process Mixture of regression. The extension assumes that each customer belongs probabilistically to different mixtures of regression, thereby permitting us to estimate a different impact of customer characteristic variables for each customer. Our model creates several customer groups to mirror the structure of the target data set. The effectiveness of our proposal is confirmed by a comparison involving a real e-commerce transaction dataset and an artificial dataset; it generally achieves higher predictive performance. In addition, we show that preselecting the actual number of customer groups does not always lead to higher predictive performance.