The Annals of Statistics

Nonparametric Bayesian estimators for counting processes

Yongdai Kim

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Abstract

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.

Article information

Source
Ann. Statist., Volume 27, Number 2 (1999), 562-588.

Dates
First available in Project Euclid: 5 April 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1018031207

Digital Object Identifier
doi:10.1214/aos/1018031207

Mathematical Reviews number (MathSciNet)
MR1714717

Zentralblatt MATH identifier
0980.62078

Subjects
Primary: 62C10: Bayesian problems; characterization of Bayes procedures
Secondary: 60G55: Point processes

Keywords
Nonparametric Bayesian estimator multiplicative counting process Lévy process.

Citation

Kim, Yongdai. Nonparametric Bayesian estimators for counting processes. Ann. Statist. 27 (1999), no. 2, 562--588. doi:10.1214/aos/1018031207. https://projecteuclid.org/euclid.aos/1018031207


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