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Abstract:
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First passage distributions in multistate models are used to answer important research questions. A popular multistate model is the semi-Markov process (SMP). An SMP has defined states, and often modelers choose parametric distributions to represent the waiting time from transitioning from one state to another. However in some situations, modelers may not want to make parametric assumptions about transition distributions. Also, in processes with many states it is challenging to choose an appropriate distributions for each possible transition. To address these and other situations, we propose a Bayesian nonparametric method to model the waiting time between states. This method assumes a Dirichlet Process (DP) prior on each state to state waiting time distribution. The DPs are then updated with the collected data. The first passage distribution from one state to another is then a convolution and mixture of these posterior processes. Our method computes and makes inference on these first passage processes in semi-Markov models.
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