uniform distribution can't be sampled

[segasai]

Hi,

while adding tests I noticed that the uniform distribution fails to sample with current code. It looks like it's connected to this https://github.com/joshspeagle/dynesty/pull/203

import numpy
import dynesty

# seed the random number generator
np.random.seed(5647)

nlive = 1000
printing = True

def loglike(x):
    return 0

def prior_transform(x):
    return x

def test_sample():
    ndim = 2
    sampler = dynesty.NestedSampler(loglike,
                                    prior_transform,
                                    ndim,
                                    nlive=nlive,
                                    bound='multi',
                                    sample='unif')
    sampler.run_nested(dlogz=0.1, print_progress=printing)
    logz_truth = 0
    # this the integral
    logz, logzerr = sampler.results.logz[-1], sampler.results.logzerr[-1]
    thresh = 5
    assert ((logz - logz_truth) < thresh * logzerr)

I don't actually know what's the fix here.

[segasai]

It looks like https://github.com/joshspeagle/dynesty/blob/858bb15dedcff600617cecb77fd6f3f2cc9fb3c9/dynesty/sampler.py#L379 here there is basically an infinite loop when all the likelihood values are the same.

Also, I remember reading something in arxiv about this: https://arxiv.org/abs/2010.13884 So apparently in multinest there are tiny perturbations to logl values that resolve that issue (which are technically not quite right)

[joshspeagle]

Yes, this is a fundamental issue with nested sampling -- it can't deal with likelihood slabs (it requires a unique mapping from a particular likelihood value L to a particular prior volume X, which is broken if this is a region rather than a contour). The tiny perturbations might be a practical fix to this problem, but it's an edge case for sure.

[segasai]

I think one potential way of dealing in practice is to at least raise a warning if all the likelihood values of live-points are exactly the same and proposal fails for many iterations to alarm the user of the problem.

[joshspeagle]

Yea, this is a good idea. I'll put a note down to add a check, flag, and warning for users if it looks like we've hit this particular edge-case.

[ghost]

I'm having a problem where I think it's possible that there are regions of similar likelihood values causing difficulties with sampling. I have looked through the code but I'm not sure I understand how to return and check the likelihood values of live points to diagnose the problem; would it be possible for any advice on how to go about this until the fix is implemented? Thanks

[joshspeagle]

You should be able to access the live points directly using the sampler.live_[u,v,logl] which correspond to their locations in the unit cube, transformed position, and log-likelihood, respectively.