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We explore the concept of a consistent exchangeable survival process - ajoint distribution of survival times in which the risk set evolves as acontinuous-time Markov process with homogeneous transition rates. We show acorrespondence with the de Finetti approach of constructing an exchangeablesurvival process by generating iid survival times conditional on a completelyindependent hazard measure. We describe several specific processes, showing howthe number of blocks of tied failure times grows asymptotically with the numberof individuals in each case. In particular, we show that the set of Markovsurvival processes with weakly continuous predictive distributions can becharacterized by a two-dimensional family called the harmonic process. We endby applying these methods to data, showing how they can be easily extended tohandle censoring.

Weak continuity of predictive distribution for Markov survival processes