A Nonhomogeneous Poisson process predictive model using maximum entropy prior random effects with application to predict purchases

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Top-tier customers -that is, those 20% of customers that typically bring in 80% of all profits- are extremely valuable to companies. In the many instances in which organizations attribute top-tier status to customers based on their consumption behaviour within a specific period, such as a year, it becomes very important to determine, during this period, how likely those gold customers are to retain their top-tier status going into the next period. This allows better planning at the corporate level, but can also allow for corrective measures or special retention efforts to be deployed. For this, we develop a model of intra-periodic forecasting of customer behaviour that allows for a continuous re-estimation of customer status or value according to calendar time, based on historical data and year-to-date information rather than existing models that predict customer churn or customer lifetime value either at the beginning of a period or on a continuous basis according to the evolution of inter-purchase time. Our model uses nonhomogeneous Poisson processes with possible heterogeneity amongst the individual units modeled with higher moment maximum entropy prior random effects instead of the gamma prior. We empirically assess the performance of such a model with a real data set from a loyalty program at a major commercial airline and compared its adequacy to the negative binomial model using the conjugate gamma prior.

, 17 pages

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