Applications of Bayesian analysis of stochastic processes

Bayesian methods provide a natural framework for the analysis of data that become sequentially available, either for descriptive, predictive or prescriptive purposes. We discuss two applications that demonstrate this. The first one concerns warranty claim data of appliances in the field. A dynamic model for count data and particle filter methods are used for predicting the number of future claims. The second one concerns the monitoring of high-quality processes, where an out-of-control decision is taken based on the predictive distribution of time between events.