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

TL;DR

This paper develops a Bayesian nonparametric method for estimating a concave distribution function from mixed interval censored data, ensuring consistency and demonstrating effectiveness through simulations and real data applications.

Contribution

It introduces a novel Bayesian approach for concave distribution estimation with mixed interval censored data, including conditions for prior consistency and computational techniques.

Findings

Method is consistent under specified prior conditions.

Computational algorithms effectively sample from the posterior.

Performance validated through simulations and real datasets.

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.