Efficiency comparison among different sampling schemes (BPS, Zigzag-HMC, LG-HMC, LG-NUTS).

We calculate effective sample size (ESS) per hour run-time for the elements of C, R, X, log joint density log p(X, Ω), and likelihood l(X, Ω). For the three multivariate parameters (C, R, X) with dimensions 276, 276, and 11,235, respectively, we report the minimal ESS across all dimensions. We conduct three independent simulations for each method and report the ESS values in the first three rows. We include the mean and standard deviation in the last row for each method to provide a summary of its overall performance. The bold number indicates the highest value in each of the five columns. For BPS, given the larger number of iterations required to achieve convergence, we record one sample of X every 1,000 iterations to comply with storage limitations, and report upper bounds of the actual ESS by multiplying the ESS from thinned samples by 1,000.