Table 5: Comparison of the 25 best LC-PFN and MCMC-PP variants on prior curves in terms of log-likelihood (higher is better) at  $10\%$ ,  $20\%$ ,  $40\%$ , and  $80\%$  cutoffs. Values in brackets correspond to one standard error.
Method	Parameters	10%	20%	40%	80%	Avg. Runtime (s)
MCMC-PP	nsamples=2000, nwalkers=100, burn-in=500, thin=10	1.628 (0.01)	1.939 (0.011)	2.265 (0.01)	2.469 (0.009)	29.944 (7.6E-01)
MCMC-PP	nsamples=2000, nwalkers=100, burn-in=500, thin=1	1.628 (0.01)	1.939 (0.011)	2.265 (0.01)	2.469 (0.009)	54.401 (3.1E-01)
MCMC-PP	nsamples=4000, nwalkers=50, burn-in=0, thin=10	1.629 (0.01)	1.942 (0.011)	2.266 (0.009)	2.467 (0.009)	28.783 (6.2E-01)
MCMC-PP	nsamples=4000, nwalkers=50, burn-in=0, thin=1	1.629 (0.01)	1.943 (0.011)	2.266 (0.009)	2.467 (0.009)	53.292 (4.3E-01)
MCMC-PP	nsamples=4000, nwalkers=50, burn-in=50, thin=100	1.629 (0.01)	1.943 (0.011)	2.266 (0.009)	2.467 (0.009)	26.672 (7.3E-01)
MCMC-PP	nsamples=4000, nwalkers=50, burn-in=100, thin=100	1.631 (0.01)	1.943 (0.011)	2.267 (0.009)	2.469 (0.009)	26.997 (7.4E-01)
MCMC-PP	nsamples=4000, nwalkers=50, burn-in=50, thin=10	1.631 (0.01)	1.944 (0.011)	2.267 (0.009)	2.468 (0.009)	29.109 (6.3E-01)
MCMC-PP	nsamples=4000, nwalkers=50, burn-in=50, thin=1	1.631 (0.01)	1.944 (0.011)	2.267 (0.009)	2.469 (0.009)	53.601 (4.2E-01)
MCMC-PP	nsamples=4000, nwalkers=50, burn-in=100, thin=10	1.632 (0.01)	1.943 (0.011)	2.268 (0.01)	2.47 (0.009)	29.433 (6.4E-01)
MCMC-PP	nsamples=4000, nwalkers=50, burn-in=100, thin=1	1.632 (0.01)	1.943 (0.011)	2.268 (0.01)	2.47 (0.009)	53.941 (4.2E-01)
MCMC-PP	nsamples=4000, nwalkers=50, burn-in=500, thin=100	1.632 (0.01)	1.94 (0.012)	2.274 (0.01)	2.477 (0.009)	29.601 (8.2E-01)
MCMC-PP	nsamples=4000, nwalkers=50, burn-in=500, thin=10	1.632 (0.01)	1.942 (0.011)	2.275 (0.01)	2.477 (0.009)	32.036 (7.1E-01)
MCMC-PP	nsamples=4000, nwalkers=50, burn-in=500, thin=1	1.632 (0.01)	1.942 (0.011)	2.275 (0.01)	2.477 (0.009)	56.526 (3.4E-01)
MCMC-PP	nsamples=4000, nwalkers=100, burn-in=0, thin=100	1.637 (0.01)	1.954 (0.011)	2.274 (0.01)	2.474 (0.009)	44.076 (1.4E+00)
MCMC-PP	nsamples=4000, nwalkers=100, burn-in=0, thin=10	1.639 (0.01)	1.956 (0.011)	2.276 (0.01)	2.476 (0.009)	48.947 (1.2E+00)
MCMC-PP	nsamples=4000, nwalkers=100, burn-in=0, thin=1	1.639 (0.01)	1.956 (0.011)	2.276 (0.01)	2.476 (0.009)	98.033 (9.9E-01)
MCMC-PP	nsamples=4000, nwalkers=100, burn-in=50, thin=100	1.639 (0.01)	1.956 (0.011)	2.276 (0.01)	2.476 (0.009)	44.618 (1.4E+00)
MCMC-PP	nsamples=4000, nwalkers=100, burn-in=50, thin=10	1.64 (0.01)	1.958 (0.011)	2.277 (0.01)	2.477 (0.009)	49.475 (1.2E+00)
MCMC-PP	nsamples=4000, nwalkers=100, burn-in=50, thin=1	1.64 (0.01)	1.958 (0.011)	2.277 (0.01)	2.477 (0.009)	98.548 (1.0E+00)
MCMC-PP	nsamples=4000, nwalkers=100, burn-in=50, thin=100	1.641 (0.01)	1.958 (0.011)	2.277 (0.01)	2.477 (0.009)	45.16 (1.4E+00)
MCMC-PP	nsamples=4000, nwalkers=100, burn-in=100, thin=10	1.641 (0.01)	1.957 (0.011)	2.278 (0.01)	2.478 (0.009)	50.011 (1.2E+00)
MCMC-PP	nsamples=4000, nwalkers=100, burn-in=100, thin=1	1.641 (0.01)	1.957 (0.011)	2.278 (0.01)	2.478 (0.009)	98.98 (1.1E+00)
MCMC-PP	nsamples=4000, nwalkers=100, burn-in=500, thin=100	1.642 (0.01)	1.955 (0.011)	2.284 (0.01)	2.485 (0.009)	49.5 (1.6E+00)
MCMC-PP	nsamples=4000, nwalkers=100, burn-in=500, thin=10	1.642 (0.01)	1.956 (0.011)	2.285 (0.01)	2.486 (0.009)	54.328 (1.3E+00)
MCMC-PP	nsamples=4000, nwalkers=100, burn-in=500, thin=1	1.642 (0.01)	1.956 (0.011)	2.285 (0.01)	2.486 (0.009)	103.151 (1.1E+00)
LC-PFN	Nb data=100k, nlayers=6, emsize=128	1.242 (0.001)	1.508 (0.001)	1.652 (0.001)	1.709 (0.002)	0.007 (4.6E-04)
LC-PFN	Nb data=100k, nlayers=12, emsize=128	1.254 (0.001)	1.522 (0.001)	1.669 (0.001)	1.73 (0.002)	0.012 (8.3E-04)
LC-PFN	Nb data=100k, nlayers=6, emsize=256	1.267 (0.002)	1.597 (0.001)	1.764 (0.001)	1.843 (0.002)	0.011 (8.2E-04)
LC-PFN	Nb data=100k, nlayers=12, emsize=256	1.384 (0.001)	1.664 (0.001)	1.833 (0.001)	1.9 (0.002)	0.021 (1.6E-03)
LC-PFN	Nb data=100k, nlayers=3, emsize=512	1.392 (0.001)	1.679 (0.001)	1.871 (0.001)	1.959 (0.002)	0.016 (1.4E-03)
LC-PFN	Nb data=100k, nlayers=6, emsize=512	1.439 (0.001)	1.745 (0.001)	1.947 (0.001)	2.034 (0.002)	0.028 (2.5E-03)
LC-PFN	Nb data=100k, nlayers=12, emsize=512	1.504 (0.001)	1.817 (0.001)	2.013 (0.001)	2.091 (0.002)	0.048 (4.2E-03)
LC-PFN	Nb data=1M, nlayers=3, emsize=128	1.528 (0.001)	1.894 (0.001)	2.159 (0.001)	2.279 (0.002)	0.004 (2.8E-04)
LC-PFN	Nb data=1M, nlayers=6, emsize=128	1.581 (0.001)	1.949 (0.001)	2.202 (0.001)	2.308 (0.002)	0.007 (4.6E-04)
LC-PFN	Nb data=1M, nlayers=3, emsize=256	1.583 (0.001)	1.967 (0.001)	2.239 (0.001)	2.357 (0.002)	0.007 (5.0E-04)
LC-PFN	Nb data=10M, nlayers=3, emsize=128	1.585 (0.001)	1.989 (0.001)	2.282 (0.002)	2.431 (0.003)	0.004 (2.8E-04)
LC-PFN	Nb data=1M, nlayers=12, emsize=128	1.621 (0.001)	1.982 (0.001)	2.223 (0.001)	2.326 (0.002)	0.012 (8.2E-04)
LC-PFN	Nb data=1M, nlayers=3, emsize=512	1.624 (0.001)	2.011 (0.001)	2.291 (0.001)	2.417 (0.002)	0.016 (1.4E-03)
LC-PFN	Nb data=1M, nlayers=6, emsize=256	1.627 (0.001)	2.007 (0.001)	2.269 (0.001)	2.381 (0.002)	0.012 (8.7E-04)
LC-PFN	Nb data=10M, nlayers=3, emsize=256	1.654 (0.001)	2.044 (0.001)	2.347 (0.002)	2.493 (0.003)	0.006 (4.7E-04)
LC-PFN	Nb data=1M, nlayers=12, emsize=256	1.667 (0.001)	2.035 (0.001)	2.294 (0.001)	2.406 (0.002)	0.02 (1.5E-03)
LC-PFN	Nb data=1M, nlayers=6, emsize=512	1.672 (0.001)	2.051 (0.001)	2.323 (0.001)	2.441 (0.002)	0.028 (2.4E-03)
LC-PFN	Nb data=10M, nlayers=6, emsize=128	1.673 (0.001)	2.058 (0.001)	2.352 (0.001)	2.478 (0.003)	0.007 (4.6E-04)
LC-PFN	Nb data=1M, nlayers=12, emsize=512	1.699 (0.001)	2.072 (0.001)	2.344 (0.001)	2.46 (0.002)	0.051 (4.6E-03)
LC-PFN	Nb data=10M, nlayers=3, emsize=512	1.707 (0.001)	2.083 (0.001)	2.378 (0.002)	2.517 (0.003)	0.017 (1.4E-03)
LC-PFN	Nb data=1M, nlayers=12, emsize=128	1.717 (0.001)	2.094 (0.001)	2.377 (0.001)	2.498 (0.003)	0.012 (8.1E-04)
LC-PFN	Nb data=1M, nlayers=6, emsize=256	1.721 (0.001)	2.098 (0.001)	2.387 (0.002)	2.514 (0.003)	0.011 (8.2E-04)
LC-PFN	Nb data=1M, nlayers=6, emsize=512	1.744 (0.001)	2.125 (0.001)	2.404 (0.002)	2.527 (0.003)	0.026 (2.3E-03)
LC-PFN	Nb data=1M, nlayers=12, emsize=256	1.746 (0.001)	2.124 (0.001)	2.403 (0.001)	2.522 (0.003)	0.02 (1.5E-03)
LC-PFN	Nb data=1OM, nlayers=12, emsize=512	1.758 (0.001)	2.133 (0.001)	2.403 (0.002)	2.519 (0.003)	0.05 (4.5E-03)