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Keywords

BG/NBD model; Markov Chain Monte Carlo; customer lifetime value; uncertainty quantification; non-contractual customer relationships; casino analytics

Disciplines

Gaming and Casino Operations Management | Gaming Law

Document Type

Original Research Article

Abstract

The Beta-Geometric/Negative Binomial Distribution (BG/NBD) model of Fader et al. (2005) is used to describe repeat-transaction behavior in non-contractual settings: a latent visitation rate, heterogeneous across customers, governs how of- ten a customer transacts while active, and a latent dropout probability, also het- erogeneous, governs when a customer permanently churns. In its classical form, BG/NBD is estimated using maximum likelihood, producing single point estimates of the underlying population parameters and, from these, point estimates of each customer’s individual behavior. This paper develops the model from first princi- ples as a fully Bayesian framework, estimated using Markov Chain Monte Carlo (MCMC), and makes explicit a result of this approach that is left implicit: uncer- tainty in the population-level parameters propagates directly into each customer’s individual posterior distributions, rather than collapsing to a single conjugate value. We derive the model’s two mixture components, assemble the joint likelihood used for estimation, and show how a population-level posterior sample is converted into a full posterior distribution, not merely a point estimate, for every individual cus- tomer’s latent behavioral state. This foundational paper establishes the notation, derivations, and estimation framework on which a companion series of papers is based, applying the framework to derive full posterior probability distributions of individual guest churn risk, visitation, and future worth.

Funding Sources

None

Competing Interests

None

Permissions

All

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