Making ideal decisions as a product leader in a web-facing company is incredibly challenging. Beyond navigating the ambiguity of customer satisfaction and achieving business goals, leaders must also ensure their products and services remain relevant, desirable, and profitable. Data and experimentation are crucial for testing product hypotheses and informing decisions. Online controlled experiments, such as A/B testing, can provide highly reliable data to support decisions. However, these experiments can be time-consuming and costly, particularly when assessing impacts on key business metrics like retention or long-term value.

Driven by applications in clinical medicine and business, we address the problem of modeling trajectories over multiple states. We build on well-known methods from survival analysis and introduce a family of sequence models based on localized Bayesian Markov chains. We develop inference and prediction algorithms, and we apply the model to real-world data, demonstrating favorable empirical results. Our approach provides a practical and effective alternative to plain Markov chains and to existing (finite) mixture models; It retains the simplicity and computational benefits of the former while matching or exceeding the predictive performance of the latter.

Online controlled experiments, in which different variants of a product are compared based on an Overall Evaluation Criterion (OEC), have emerged as a gold standard for decision making in online services. It is vital that the OEC is aligned with the overall goal of stakeholders for effective decision making. However, this is a challenge when the overall goal is not immediately observable. For instance, we might want to understand the effect of deploying a feature on long-term retention, where the outcome (retention) is not observable at the end of an A/B test.