  This article proposes an efficient Bayesian inference for piecewise
exponential hazard (PEH) models, which allow the effect of a covariate on the
survival time to vary over time. The proposed inference methodology is based on
a particle smoothing (PS) algorithm that depends on three particle filters.
Efficient proposal (importance) distributions for the particle filters tailored
to the nature of survival data and PEH models are developed using the Laplace
approximation of the posterior distribution and linear Bayes theory. The
algorithm is applied to both simulated and real data, and the results show that
it generates an effective sample size that is more than two orders of magnitude
larger than a state-of-the-art MCMC sampler for the same computing time, and
scales well in high-dimensional and relatively large data.
