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Nonparametric Priors for Vectors of Survival Functions

By Ilenia Epifani and Antonio Lijoi

Abstract

The paper proposes a new nonparametric prior for two–dimensional vectors of survival functions (S1, S2). The definition we introduce is based on the notion of L´evy copula and it will be used to model, in a nonparametric Bayesian framework, two–sample survival data. Such an application will yield a natural extension of the more familiar neutral to the right process of Doksum (1974) adopted for drawing inferences on single survival functions. We, then, obtain a description of the posterior distribution of (S1, S2), conditionally on possibly right–censored data. As a by–product of our analysis, we find out that the marginal distribution of a pair of observations from the two samples coincides with the Marshall–Olkin or the Weibull distribution according to specific choices of the marginal L´evy measures.Bayesian nonparametrics, Completely random measures, Dependent stable processes, L´evy copulas, Posterior distribution, Right–censored data, Survival function

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Provided by: Research Papers in Economics
Downloaded from http://economia.unipv.it/docs/dipeco/quad/ps/RePEc/pav/wpaper/q098.pdf

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  1. (1981). A Bayesian nonparametric approach to reliability.
  2. (2007). A Bayesian semi-parametric bivariate failure time model.
  3. (2003). A bivariate Dirichlet process.
  4. (1990). A survey of product-integration with a view toward application in survival analysis.
  5. (2004). An ANOVA model for dependent random measures.
  6. (2009). Asymptotics for posterior hazards.
  7. (2006). Bayesian bivariate survival estimation.
  8. (1979). Bayesian nonparametric estimation based on censored data.
  9. (2005). Bayesian Poisson process partition calculus with an application to Bayesian L´ evy moving averages.
  10. (1997). Beta-Stacy processes and a generalization of the P´ olya-urn scheme.
  11. (1971). Bivariate failure rate.
  12. (2006). Characterization of dependence of multidimensional L´ evy processes using L` evy copulas.
  13. (2001). Decision theoretic aspects of dependent nonparametric processes. In Bayesian methods with applications to science, policy and official statistics
  14. (2003). Dependence structure of spectrally positive multidimensional L´ evy processes. Unpublished Manuscript.
  15. (2000). Dependent Dirichlet processes.
  16. (1999). Dependent nonparametric processes.
  17. (2004). Financial modelling with jump processes. Chapman & Hall/CRC,
  18. (2008). Kernel stick-breaking processes
  19. (1990). Nonparametric Bayes estimators based on beta processes in models for life history data.
  20. (1989). On a class of Bayesian nonparametric estimates. II. Hazard rate estimates.
  21. (2001). On posterior consistency of survival models.
  22. (2006). Order-based dependent Dirichlet processes.
  23. (1993). Poisson processes.
  24. (2008). Posterior analysis for some classes of nonparametric models.
  25. (1974). Prior distributions on spaces of probability measures.
  26. (1980). Rank tests for censored matched pairs,
  27. (2008). Series representations for multivariate generalized gamma processes via a scale invariance principle.
  28. (2003). Some aspects of neutral to the right priors.
  29. (1974). Tailfree and neutral random probabilities and their posterior distributions.
  30. (2008). The matrix stick-breaking process: flexible Bayes meta-analysis.
  31. (2008). The nested Dirichlet process.

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