Superposition of beta processes

We consider a neutral to the right process that corresponds to the superposition of independent beta processes at the cumulative hazard level. It places a prior distribution on the survival distribution resulting from independent competing failure times. It can be derived as the infinitesimal weak limit of a discrete time process which has the conditional probability of an event at time t given survival up to t defined as the result of a series of m independent Bernoulli experiments. The continuous time version of the process, termed m-fold beta NTR process, is described in terms of completely random measures. We discuss prior specification and illustrate posterior inference on a real data example.