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Titlebook: Nonparametric Bayesian Inference; Contributions by Jea Jean-Pierre Florens,Michel Mouchart Book 2024 The Editor(s) (if applicable) and The

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Some Useful Properties of the Dirichlet Processess through independence relations between associated .-fields entails a nice description of the posterior distribution of the Dirichlet process at points where there is either no or at least one observation.
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Nonparametric Competing Risks Models: Identification and Strong Consistency3)) are used to show the almost sure convergence of simple functionals of the predictable hazard measures and of the distributions of the latent or “fictitious” independent risks. These results entails the almost sure uniform convergence on the real line of the distributions of these independent risks.
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Duration Model Bayesian Semi-parametric Approachrely random. We give some results on Gamma and Dirichlet distributions laws. In the specific case of Gamma process, we try to give some interpretation of classical results using Bayesian semi-parametric approach. As for the estimation of the nuisance parameter, we simply use an iterative expectation rule and a recurrence approach.
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Survival Data with Explanatory Processes: A Full Nonparametric Bayesian Analysister is also obtained. These posterior distributions are computed for Beta processes and Gamma processes in the proportional hazards and multiplicative intensity models. The noninformative case provides a new likelihood for the parameters even in case of ties, contrary to the Cox likelihood.
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