This text describes a method of estimating the hazard rate of survival data following monotone Aalen regression model. The proposed approach is based on techniques which were introduced by Arjas and Gasbarra \cite{gasbarra}. The unknown functional parameters are assumed to be a priori piecewise constant on intervals of varying count and size. The estimates are obtained with the aid of the Gibbs sampler and its variants. The performance of the method is explored by simulations. The results indicate that the method is applicable on small sample size datasets.
We compare alternative definitions of undirected graphical models for discrete, finite variables. Lauritzen \cite{Lauritzen:1996} provides several definitions of such models and describes their relationships. He shows that the definitions agree only when joint distributions represented by the models are limited to strictly positive distributions. Heckerman et al. \cite{Heckerman_et_al:2000}, in their paper on dependency networks, describe another definition of undirected graphical models for strictly positive distributions. They show that this definition agrees with those of Lauritzen \cite{Lauritzen:1996} again when distributions are strictly positive. In this paper, we extend the definition of Heckerman et al. \cite{Heckerman_et_al:2000} to arbitrary distributions and show how this definition relates to those of Lauritzen \cite{Lauritzen:1996} in the general case.