---
abstract: |
    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.

    **Key words**: Hazard function, Linear Bayes, particle filter, particle smoothing, piecewise exponential, Survival function.
author:
- Parfait Munezero
bibliography:
- 'Bibliography.bib'
title: Efficient Particle Smoothing for Bayesian Inference in Dynamic Survival Models
---

\
[Parfait.Munezero@stat.su.se]{}

Introduction
============

The standard model for analysing survival data is the proportional hazards model which specifies the hazard function as a product of a baseline hazard (an unknown function of time, $t$) and a relative 