I am sampling the posterior distribution in order to carry out some model
selection (much like outlined in the cookbook). Interestingly both the Bethe
as well as the mean field approximations of the posterior entropy appear to
be returning an answer of 0.0. I was thus after some opinions: Are there
cases where I might reasonably expect this to be the correct answer/how
would people check that it is not simply being caused by the approximations
not being applicable to my data set?

Differently from Bethe, the MF approximation can only return zero if the
true entropy is also zero. This means that the posterior distribution is
concentrated around a single partition with probability one, and others with
probability zero. This should only occur if the SBM is a perfect fit, e.g.
for very dense networks sampled from the SBM ensemble. For real data this
should almost never happen.

Thank you, that confirms my suspicion that something strange is going on
here. The average description length across 200,000 sweeps appears to be
roughly three times that returned by "minimize_nested_blockmodel_dl" so it
seems to me like the posterior distribution is not centered around a single
partition. Do you have any more thoughts on what might cause this? (I am
trying to compile the current git version too to see whether the problem
persists there.)

Thank you, that confirms my suspicion that something strange is going on
here. The average description length across 200,000 sweeps appears to be
roughly three times that returned by "minimize_nested_blockmodel_dl" so it
seems to me like the posterior distribution is not centered around a single
partition.

I don't see how you can conclude this from the reason given.

Do you have any more thoughts on what might cause this? (I am
trying to compile the current git version too to see whether the problem
persists there.)

It is difficult to blindly guess, without being given more information.

Thank you, that confirms my suspicion that something strange is going on
here. The average description length across 200,000 sweeps appears to be
roughly three times that returned by "minimize_nested_blockmodel_dl" so
it
seems to me like the posterior distribution is not centered around a
single
partition.

I don't see how you can conclude this from the reason given.

If I have a single peak in the posterior with a likelihood of 1 should I not
expect that sampling from the posterior and maximising the posterior
likelihood return the same value? Following that, if the average description
length obtained by sampling from the posterior is different I must have had
other partitions with non-zero probabilities contributing which contradicts
the entropy of zero. Am I making a logical mistake/missing something here?

Tiago Peixoto wrote

It is difficult to blindly guess, without being given more information.

Once i have verified whether the problem persists with the current git
version I will try and provide an MWE. The data is empirical however so I
would be surprised by a perfect fit.