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Bayesian inference for Poisson process models with censored data. (English) Zbl 1360.62441
Summary: Bayesian statistical inference for a nonhomogeneous Poisson point process model with censored data is considered. Weighted gamma process priors are found to be the natural conjugate priors for the cumulative intensity of this model. Upon deflating the prior, the posterior mean of the cumulative intensity becomes a relative of the well-known Nelson-Aalen estimator. Small- and large-sample approximations to the posterior distribution using the Bayesian bootstrap methods are discussed.

MSC:
62M07 Non-Markovian processes: hypothesis testing
62G09 Nonparametric statistical resampling methods
62N01 Censored data models
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