Multistate Analysis with Infinite Mixtures of Markov Chains

Lucas Maystre, Tiffany Wu, Roberto Sanchis Ojeda, Tony Jebara

Keywords: survival analysis, Markov chains, time-to-event, event history analysis, duration analysis, reliability analysis

TL;DR: Infinite mixtures of Markov chains are simple and effective models for multistate analysis.

Abstract: 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.