  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.
