Metropolis equivalent to NUTS target_accept?

[junpenglao]

In general this is a difficult question for Metropolis, you can have a look at these 2 related discussions:

Where do the automatic tuning values in metropolis.py come from?

I noticed that in metropolis.py there is this code in the tune function: # Switch statement if acc_rate < 0.001: # reduce by 90 percent scale *= 0.1 elif acc_rate < 0.05: # reduce by 50 percent scale *= 0.5 elif acc_rate < 0.2: # reduce by ten percent scale *= 0.9 elif acc_rate > 0.95: # increase by factor of ten scale *= 10.0 elif acc_rate > 0.75: # increase by double scale *= 2.0 elif acc_rate > 0.5: # increase by ten percent scale *= 1.1 Whe…

Metropolis: ideal balance between slow-mixing and high rejection rate?

I’m using PyMC’s Metropolis to sample from a 200-dimensional probability distribution and I want it to converge faster by setting the scale of the proposal distribution “just right”. Here’s what I did: Lots of trial and error and got an estimation of the variance of the target distribution. I used it to derive a proposal distribution with balanced scales among dimensions. (So the proposal distribution mimics the proportions of the target distribution). I calculated the radius of the typical se…

For NUTS and HMC, I think the value is empirically works fine, but there is also no theory behind it.