Bayesian nonparametric estimation in the current status continuous mark model

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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 (Formula presented.). Our main result shows that under appropriate conditions, the posterior distribution function contracts pointwisely at rate (Formula presented.) if the true density is (Formula presented.) -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.