  Bayesian nonparametric inferential procedures based on Markov chain Monte
Carlo marginal methods typically yield point estimates in the form of posterior
expectations. Though very useful and easy to implement in a variety of
statistical problems, these methods may suffer from some limitations if used to
estimate non-linear functionals of the posterior distribution. The main goal of
the present paper is to develop a novel methodology that extends a
well-established marginal procedure designed for hazard mixture models, in
order to draw approximate inference on survival functions that is not limited
to the posterior mean but includes, as remarkable examples, credible intervals
and median survival time. Our approach relies on a characterization of the
posterior moments that, in turn, is used to approximate the posterior
distribution by means of a technique based on Jacobi polynomials. The
inferential performance of our methodology is analyzed by means of an extensive
study of simulated data and real data consisting of leukemia remission times.
Although tailored to the survival analysis context, the procedure we introduce
can be adapted to a range of other models for which moments of the posterior
distribution can be estimated.
