Clarify Wishart warning messaging

[yejiming]

Summary

• clarify the pm.Wishart docstring to explain that PyMC can evaluate its log-probability but it should not be used as a covariance prior in models
• align the runtime warning with that wording and keep the LKJ alternatives explicit
• update Wishart warning assertions in the distribution tests and shared test helpers

Testing

• HOME=/tmp XDG_CACHE_HOME=/tmp MPLCONFIGDIR=/tmp .venv/bin/python -m pytest tests/distributions/test_multivariate.py -k Wishart -q

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Documentation build overview

📚 pymc | 🛠️ Build #32021820 | 📁 Comparing f66f118 against latest (0f5c0ca)

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Show files changed (26 files in total): 📝 26 modified | ➕ 0 added | ➖ 0 deleted

File	Status
glossary.html	📝 modified
contributing/developer_guide.html	📝 modified
_modules/pymc/pytensorf.html	📝 modified
_modules/pymc/testing.html	📝 modified
api/generated/pymc.draw.html	📝 modified
api/generated/pymc.icdf.html	📝 modified
api/generated/pymc.logcdf.html	📝 modified
api/generated/pymc.logp.html	📝 modified
api/generated/pymc.sample_posterior_predictive.html	📝 modified
api/generated/pymc.sample_prior_predictive.html	📝 modified
_modules/pymc/distributions/continuous.html	📝 modified
_modules/pymc/distributions/distribution.html	📝 modified
_modules/pymc/distributions/multivariate.html	📝 modified
_modules/pymc/distributions/shape_utils.html	📝 modified
_modules/pymc/logprob/basic.html	📝 modified
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_modules/pytensor/tensor/basic.html	📝 modified
_modules/pytensor/tensor/math.html	📝 modified
api/distributions/generated/pymc.Wishart.html	📝 modified
api/distributions/generated/classmethods/pymc.SymbolicRandomVariable.update.html	📝 modified
api/model/generated/classmethods/pymc.model.core.Model.compile_fn.html	📝 modified

[twiecki]

Well technically it should not be used as a prior, period, not just for covariance matrices, no?

[ricardoV94]

Well technically it should not be used as a prior, period, not just for covariance matrices, no?

Depends what you are going to sample it with. If it's forward only it's fine, if you have a custom sampler it's fine, if you have a custom transform it's fine.

Maybe you are not even going to sample it, just evaluate a model logp for whatever purposes you want. Maybe you just want a pretty grahpviz...

This warning is too opinionated.

[ricardoV94]

Ah I jumped too fast, yes. In that context, it shouldn't be used as a prior period, doesn't matter what that prior is used for next