de Blasi, Pierpaolo; Peccati, Giovanni; Prünster, Igor Asymptotics for posterior hazards. (English) Zbl 1168.62042 Ann. Stat. 37, No. 4, 1906-1945 (2009). Summary: An important issue in survival analysis is the investigation and the modeling of hazard rates. Within a Bayesian nonparametric framework, a natural and popular approach is to model hazard rates as kernel mixtures with respect to a completely random measure. We provide a comprehensive analysis of the asymptotic behavior of such models. We investigate the consistency of the posterior distribution and derive fixed sample size central limit theorems for both linear and quadratic functionals of the posterior hazard rate. The general results are then specialized to various specific kernels and mixing measures yielding consistency under minimal conditions and neat central limit theorems for the distribution of functionals. Cited in 13 Documents MSC: 62G20 Asymptotic properties of nonparametric inference 62F15 Bayesian inference 60F05 Central limit and other weak theorems 60G57 Random measures Keywords:asymptotics; Bayesian consistency; Bayesian nonparametrics; central limit theorem; completely random measure; path-variance; random hazard rate; survival analysis PDFBibTeX XMLCite \textit{P. de Blasi} et al., Ann. Stat. 37, No. 4, 1906--1945 (2009; Zbl 1168.62042) Full Text: DOI arXiv References: [1] Barron, A., Schervish, M. J. and Wasserman, L. (1999). The consistency of distributions in nonparametric problems. Ann. Statist. 27 536-561. · Zbl 0980.62039 · doi:10.1214/aos/1018031206 [2] Brix, A. (1999). Generalized gamma measures and shot-noise Cox processes. Adv. in Appl. Prob. 31 929-953. · Zbl 0957.60055 · doi:10.1239/aap/1029955251 [3] Daley, D. and Vere-Jones, D. J. (1988). An Introduction to the Theory of Point Processes . Springer, New York. · Zbl 0657.60069 [4] Doksum, K. (1974). 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