models. Further, the comparison of PSLiB and the auxiliary mixture sampler (AMS) of @wagner2011bayesian shows that PSLiB outperforms AMS in terms of both the effective sample size and the computation time.

The rest of the paper is organized as follows. The next section delineates the likelihood and prior for the dynamic survival model. Section 3 presents the proposed inference methodology and, in Section 4, the performance of PSLiB is assessed through simulated and observed data. Finally, some concluding remarks and suggestions for future research are provided in Section \[sec:Concluding-remarks\].

Dynamic survival model specification\[sec:Dynamic-Survival-Models\]
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Let $\tilde{T}$ denote a random variable representing the survival time, which is the time until an event of interest occurs. Usually the survival time is not observed for all individuals participating in the study: some individuals are lost before they have experienced the event or, for some, the study ends before they experience the event. Individuals whose survival time is not known are called (right) *censored* observations. Letting the random variable $C$ denote the censoring time, the observed survival time is represented by the random variable $T=\min(\tilde{T},C)$.

The *hazard function* describes the instantaneous rate at which the event occurs, and it can be linked to the 