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.