Bayesian nonparametric estimation in the current status continuous mark model. (31st December 2021)

• Record Type: Journal Article
• Authors: Jongbloed, Geurt; van der Meulen, Frank H.; Pang, Lixue
• Is Part Of: Scandinavian journal of statistics. Volume 49:Number 3(2022)
• Page Start: 1329
• Page End: 1352
• Publication Date: 2021-12-31
• Subjects: Bayesian nonparametrics -- censoring -- contraction rate -- Graph–Laplacian; Statistics -- Periodicals; 310
• DOI: 10.1111/sjos.12562
• Languages: English
• ISSNs: 0303-6898

Abstract

Abstract: We consider the current status continuous mark model where, if an event takes place before an inspection time T a "continuous mark" variable is observed as well. A Bayesian nonparametric method is introduced for estimating the distribution function of the joint distribution of the event time ( X ) and mark variable ( Y ). We consider two histogram‐type priors on the density of ( X, Y ) . Our main result shows that under appropriate conditions, the posterior distribution function contracts pointwisely at rate n / log n − ρ 3 ( ρ + 2 ) if the true density is ρ ‐Hölder continuous. In addition to our theoretical results we provide efficient computational methods for drawing from the posterior relying on a noncentered parameterization and Crank–Nicolson updates. The performance of the proposed methods is illustrated in several numerical experiments.