Open Binbose opened 1 month ago
UltraNest reports here -0.117 +- 0.019, so within these uncertainties both outputs agree.
If you want smaller uncertainties from nested sampling, you would need to crank up the number of live points. I am not sure for what purpose one needs logZ with extremely high accuracy though.
Regarding speed, with a slice sampler this is determined by the number of steps, so this is a parameter you could play with, in addition to the direction proposal.
Probably as you go to more parameters, you will find Vegas to be slower than ultranest.
I am trying to calculate the partition function of two particles interacting in the Lennard-Jones potential. I implemented the integral both with UltraNest and with torchquad. With torchquad I get logZ = -0.114 (after a couple seconds) both with Vegas Monte Carlo integration and 3 random seeds and the deterministic Boole strategy. This makes me believe that the torchquad result should be correct. However using UltraNest I get a logZ of about -0.117 after an hour of compute, so now I am unsure what algorithm to believe (and in case torchquad is correct, why UltraNest doesnt converge correctly/so slowly). Maybe I have to use different settings for UltraNest? This is my UltraNest code:
If used with 1500 live points it results in this output:
For comparison, this is my torchquad code:
resulting in