A0973
Title: Distribution splicing via Bayesian non-parametric methods
Authors: Jorge Gonzalez Cazares - IIMAS-UNAM (Mexico) [presenting]
Martin Bladt - University of Copenhagen (Denmark)
Abstract: An objective-based Bayesian non-parametric framework for studying time-to-event data is proposed, where the prior distribution is allowed to depend on an additional random source, and may update with the sample size. Such scenarios are natural, for instance, when considering empirical Bayes techniques or dynamic expert information. Conditionally inhomogeneous independent increment processes are used with non-decreasing sample paths. The asymptotic behavior is studied by showing that Bayesian consistency and Bernstein-von-Mises theorems may be recovered under suitable conditions on the asymptotic negligibility of the stochastic prior sequences. The non-asymptotic behavior of the posterior is also considered. Namely, upon conditioning, an efficient and exact simulation algorithm for the paths of the beta Levy process is provided. As a natural application, it is shown how the model can provide an appropriate definition of non-parametric spliced models, targeting data where an accurate global description of both the body and tail of the distribution is desirable. The Bayesian non-parametric nature of the proposed estimators can offer conceptual and numerical alternatives to their parametric counterparts.
