  Bayesian nonparametric marginal methods are very popular since they lead to
fairly easy implementation due to the formal marginalization of the
infinite-dimensional parameter of the model. However, the straightforwardness
of these methods also entails some limitations: they typically yield point
estimates in the form of posterior expectations, but cannot be used to estimate
non-linear functionals of the posterior distribution, such as median, mode or
credible intervals. This is particularly relevant in survival analysis where
non-linear functionals such as e.g. the median survival time, play a central
role for clinicians and practitioners. The main goal of this paper is to
summarize the methodology introduced in [Arbel et al., Comput. Stat. Data. An.,
2015] for hazard mixture models in order to draw approximate Bayesian inference
on survival functions that is not limited to the posterior mean. In addition,
we propose a practical implementation of an R package called momentify designed
for moment-based density approximation, and, by means of an extensive
simulation study, we thoroughly compare the introduced methodology with
standard marginal methods and empirical estimation.
