the particle smoother with linear Bayes proposals (PSLiB). The PSLiB algorithm is straightforward to implement since one needs only the Laplace approximation of the posterior of hazard function, and it can be easily extended to the class of multi-parameter regression models for survival data [@burke2017multi] which model the survival time parametrically with each distributional parameter allowed to depend a set of covariates. Here, the only requirements would be the Laplace approximation of the posterior distribution of the distributional parameters with respect to the linear predictors.

The proposed inference methodology is applied to both simulated and real data. The simulation study, presented in Section \[sec:Applications\], aims at investigating the performance of PSLiB with respect to the dimension of the covariate vector, the size of the dataset, the proportion of censored observations in the data, and the length of the study period. Results show that PSLiB is highly efficient in high-dimensional data and fairly large data with many observations, and scales well computationally. However, the performance degrades as the number of covariates and the proportion of censored observations increase. Similar performance degradation with respect to the number of covariates in the model has been noted by @villani2012generalized in a different class of 