Improvements in information technology have made it easier for industry to communicate with their customers, raising hopes for a scheme that can estimate when customers will want to make purchases. Although a number of models have been developed to estimate the time-varying purchase probability, they are based on very restrictive assumptions such as preceding purchase-event dependence and discrete-time effect of covariates. Our preliminary analysis of real-world data finds that these assumptions are invalid: self-exciting behavior, as well as marketing stimulus and preceding purchase dependence, should be examined as possible factors influencing purchase probability. In this paper, by employing the novel idea of hierarchical time rescaling, we propose a tractable but highly flexible model that can meld various types of intrinsic history dependency and marketing stimuli in a continuous-time setting. By employing the proposed model, which incorporates the three factors, we analyze actual data, and show that our model has the ability to precisely track the temporal dynamics of purchase probability at the level of individuals. It enables us to take effective marketing actions such as advertising and recommendations on timely and individual bases, leading to the construction of a profitable relationship with each customer.

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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.

Discovering interesting behavior patterns and profiles of users as they interact with E-commerce (EC) sites is an important task for site managers. We propose a probabilistic behavior model for extracting latent classes of items that impact the users' item selections but cannot be inferred from the current knowledge of the managers. The proposed model assumes that the current knowledge is represented by categories of items that are defined in the EC site, and a user selects items depending on both of their categories and latent classes. By estimating latent classes, each of which shows items accessed by users with common interests, we can find interesting factors for explaining user behavior. We evaluate our proposed model using item-access log data observed in an EC site. The results show that our model can accurately predict users' item selection, and actually discover latent classes of items having similar latent characteristic such as "colored design" and "impression" by using item categories such as "coat" and "hat" as the current knowledge of the managers.