Nonparametric bayesian estimation of a concave distribution function with mixed interval censored data

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Abstract

Assume we observe a finite number of inspection times together with information on whether a specific event has occurred before each of these times. Suppose replicated measurements are available on multiple event times. The set of inspection times, including the number of inspections, may be different for each event. This is known as mixed case interval censored data. We consider Bayesian estimation of the distribution function of the event time while assuming it is concave. We provide sufficient conditions on the prior such that the resulting procedure is consistent from the Bayesian point of view. We also provide computational methods for drawing from the posterior and illustrate the performance of the Bayesian method in both a simulation study and two real datasets.

Original languageEnglish
Pages (from-to)544-568
Number of pages25
JournalBrazilian Journal of Probability and Statistics
Volume35
Issue number3
DOIs
Publication statusPublished - 2021

Keywords

  • Bayesian nonparametrics
  • Dirichlet process
  • Markov Chain Monte Carlo
  • Posterior consistency
  • Shape constrained inference

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