Summary: Failure times that are grouped according to shared environments arise commonly in statistical practice. That is, multiple responses may be observed for each of many units. For instance, the units might be patients or centers in a clinical trial setting. Bayesian hierarchical models are appropriate for data analysis in this context. At the first stage of the model, survival times can be modelled via the Cox partial likelihood, using a justification due to J. D. Kalbfleisch
[J. R. Stat. Soc., Ser. B 40, 214-221 (1978; Zbl 0387.62030
)]. Thus, questionable parametric assumptions are avoided. Conventional wisdom dictates that it is comparatively safe to make parametric assumptions at subsequent stages. Thus, unit-specific parameters are modelled parametrically. The posterior distribution of parameters given observed data is examined using Markov chain Monte Carlo methods. Specifically, the hybrid Monte Carlo method, as described by R. M. Neal
[Probabilistic inference using Markov chain Monte Carlo methods. Tech. Rep. CRG-TR-93-1, Dpt. Computer Sci., Univ. Toronto/Canada (1993)] is utilized.