For both PRS-CS and PRS-CS-auto, the Gibbs sampler usually attains reasonable convergence after 1000 Markov Chain Monte Carlo (MCMC) iterations and produces prediction accuracy close to what can be achieved by much longer MCMC runs. We thus use 1000 MCMC iterations with the first 500 steps as burn-in in simulation studies to reduce computational cost. In practice, we recommend using longer MCMC runs when time and computational resources permit. In the Partners HealthCare Biobank analysis, we report the predictive performance of PRS-CS and PRS-CS-auto based on 10,000 MCMC iterations in total and 5000 burn-in steps.
