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Nonparametric Bayesian estimators for counting processes. (English) Zbl 0980.62078

Summary: This paper is concerned with nonparametric Bayesian inference of the Aalen’s multiplicative counting process model [O. Aalen, ibid. 6, 701-726 (1978; Zbl 0389.62025)]. 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.

MSC:

62M09 Non-Markovian processes: estimation
62C10 Bayesian problems; characterization of Bayes procedures
60G48 Generalizations of martingales
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
62M99 Inference from stochastic processes

Citations:

Zbl 0389.62025
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References:

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