hazard (a function of the covariate vector, $\mathbf{x}$). This model assumes that the ratio of the hazards corresponding to two different covariate profiles is constant over time. However, in some situations the effect of the covariate may change over time, especially when the observation period is long.

Piecewise exponential hazard (PEH) models [@gamerman1991dynamic] allow the effect of the covariate to vary over time by assuming that both the baseline and relative hazard functions are piecewise constant over a set of disjoint and consecutive time intervals which partition the observation period. PEH models are special cases of the piecewise linear hazards models of @murray2016flexible and the more general P-spline hazard models proposed by @fahrmeir2011bayesian. Their key features are that the likelihood is tractable, and they are flexible enough to capture various shapes of the hazard function. Furthermore, they can be applied to both continuous survival time [@wagner2011bayesian] and discrete survival time [@fahrmeir1996smoothing].

Current Bayesian inference procedures for PEH models make use of Markov Chain Monte Carlo (MCMC) methods. @hemming2002parametric build on the transformation of the prior process suggested by @gamerman1998markov to design a Metropolis-Hastings (MH) algorithm with random walk proposals. @fahrmeir2011bayesian develop a MH algorithm with a multivariate Gaussian proposal defined 