Dynamic Conditional Independence Models and Markov Chain Monte Carlo Methods

In dynamic statistical modeling situations, observations arise sequentially, causing the model to expand by progressive incorporation of new data items and new unknown parameters. For example, in clinical monitoring, new patient-specific parameters are introduced with each new patient. Markov chain Monte Carlo (MCMC) might be used for posterior inference, but would need to be redone at each expansion stage. Thus such methods are often too slow for real-time implementation. By combining MCMC with importance-resampling, we show how real-time posterior updating can be effected. The proposed dynamic sampling algorithms utilize posterior samples from previous expansion stages, and exploit conditional independence between groups of parameters to allow samples of parameters no longer of interest to be discarded, such as when a patient dies or is discharged. We apply the methods to monitoring of heart transplant recipients during infection from cytomegalovirus.