This paper is concerned with nonparametric Bayesian inference of the Aalen’s multiplicative counting process model. For a desired nonparametric prior distribution of the cumulative intensity function, a class of Lévy processes is considered, and it is shown that the class of Lévy processes is conjugate for the multiplicative counting process model, and formulas for obtaining a posterior process are derived. Finally, our results are applied to several practically important models such as one point processes for right-censored data, Poisson processes and Markov processes.
"Nonparametric Bayesian estimators for counting processes." Ann. Statist. 27 (2) 562 - 588, April 1999. https://doi.org/10.1214/aos/1018031207