data with various sample sizes, number of covariates and length of the survival time. Results are averages over $50$ simulated datasets and $p_{c}=25\%$.]{}[ ]{}\[tab:Average-CPU-time\]

CPU time increases from $P=1$ to $P=5$, but then remains roughly constant from $P=5$ to $P=10$. Therefore the number of covariates in the model does not influence significantly the running time of the algorithm. The effect of increasing $J$ is also modest: When $J=26$, $p=10$ and $n=10,000$ it takes $7$ CPU minutes, but when $n$ is increased to $50,000$ the computation time rises to $37$ CPU minutes and if $n$ is increased further to $100,000$ it takes$100$ CPU minutes to run the algorithm. Thus, for fixed covariate’s dimension, the computation time of PSLiB increases approximately linearly with the sample size.

### Comparing PSLiB with AMS\[subsec:Comparing-the-PSLiB\]

This section compares the PSLiB and the MCMC algorithm in @wagner2011bayesian based on the number of effective sample size (ESS) of @carpenter1999improved, $$ESS=\frac{\sigma_{j}^{2}}{E\left(\hat{\mu}_{j}-\mu_{j}\right)^{2}},$$ where $\hat{\mu}_{j}$ is the posterior estimate of the regression coefficients computed as in (\[eq:particle approx of the posterior estimate\]), and $\mu_{j}$ and $\sigma_{j}^{2}$ are respectively the true mean and variance of the regression coefficient, which following @carpenter1999improved, are approximated by taking averages of $\hat{\mu}_{j}$ and $\hat{\sigma}_{j}^{2}$ over $M$ 