independent runs of the algorithm.

To compare both the ESS and computation time for PSLiB and AMS, ESS per computation time (in CPU seconds) is used. The ESS is computed based on $M=100$ independent replications of the PSLiB and AMS runs on a dataset generated from a DGP with $P=1$, $J=26$ and $n=1000$. The same number of iterations ($5000$ MCMC iteration/particles) is set for both algorithms. The AMS model runs with the prior settings proposed by @wagner2011bayesian.

![[Comparing the PSLiB and AMS algorithms using the ratio of ESS/sec for PSLiB and AMS. The results are computated based on $100$ independent replications of each algorithm.\[fig:Comparing PSLiB and the AMS\]]{}](Simulation_comparison_AMS_and_PSLiB)

Figure \[fig:Comparing PSLiB and the AMS\] displays the ratio of the ESS/sec for PSLiB and AMS for all regression coefficients sampled in all $J$ intervals. It is clear form Figure \[fig:Comparing PSLiB and the AMS\] that PSLiB is more efficient as it generates, on average, an effective sample size that is more than two orders of magnitudes larger than AMS (the average ratio is $133$ for $\beta_{0}$, and $131$ for $\beta_{1}$). Comparing their computation time, PSLiB takes two minutes (CPU time) while AMS takes roughly $105$ minutes. The main reason for this 