use preliz under the hood of find_constrained_prior

[aloctavodia]

In #7680 (comment) it was suggested that instead of deprecating find_constrained_prior, we should call PreliZ's maxent function.

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📚 Documentation preview 📚: https://pymc--7905.org.readthedocs.build/en/7905/

[ricardoV94]

I still think we should revisit a pymc-based implementation later on, because it wouldn't be restricted to the offers /parametrizations in preliz and you could even have symbolic inputs / fixed parameters so you can apply it to intermediate variables, now that we have symbolic MinimizeOp in PyTensor.

[ricardoV94]

Adding preliz to the env seems to have broken CI (or if not, something unrelated to this PR. We may be testing on a too old version of Python... (didn't check)

[aloctavodia]

Makes sense. I think there is no unidimensional distribution/parameterization in pymc absent in preliz. But having symbolic inputs could be interesting. Maybe something worth to try is to replace variance with entropy. While entropy is more general and the correct thing to do. Maximizing the variance should work in most cases (or some other measure of spread).

[aloctavodia]

Preliz use to have some functions that were removed and replaced for function already implemented in arviz-stats, which requieres python > 3.10

[ricardoV94]

If python 3.10 is no longer supported by the numpy NEP we can drop it here as well, but maybe worth doing in a separate PR. CC'ing @maresb in case he wants to do it and you don't have the capacity @aloctavodia ?

[ricardoV94]

Sidenote, I guess we don't have mode in Beta in PyMC? Or did I miss the feature being introduced at some point?

[aloctavodia]

I don't remember the exact date to drop 3.10, but it was in the first semester.
I also don't remember if the mode is available on PyMC, but that should not be a problem for this function to work, as the mode restraint is applied to a preliz distribution, and if the distribution does not have a mode, the user is notified.

[maresb]

I have no strong feelings. I am pretty low availability this month. I'll take care of the conda-forge updates for everything though. (Ping me if needed.)