WIP: Update LKJ notebook to not refer to Wishart #2184
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Do you have a reference for that? I thought Bartlett form is ok. |
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The warning on line https://github.com/pymc-devs/pymc3/blob/master/pymc3/distributions/multivariate.py#L550 seems like a pretty strong nudge against the Bartlett form. Maybe instead of saying the Bartlett form is highly discouraged, the LKJ is highly encouraged over the Wishart-Bartlett. |
docs/source/notebooks/LKJ.ipynb
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| "Outside of the [beta](https://en.wikipedia.org/wiki/Beta_distribution)-[binomial](https://en.wikipedia.org/wiki/Binomial_distribution) model, the multivariate normal model is likely the most studied Bayesian model in history. Unfortunately, as this [issue](https://github.com/pymc-devs/pymc3/issues/538) shows, `pymc3` cannot (yet) sample from the standard conjugate [normal-Wishart](https://en.wikipedia.org/wiki/Normal-Wishart_distribution) model. Fortunately, `pymc3` *does* support sampling from the [LKJ distribution](http://www.sciencedirect.com/science/article/pii/S0047259X09000876). This post will show how to fit a simple multivariate normal model using `pymc3` with an normal-LKJ prior.\n", | ||
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| "The normal-Wishart prior is conjugate for the multivariate normal model, so we can find the posterior distribution in closed form. Even with this closed form solution, sampling from a multivariate normal model in `pymc3` is important as a building block for more complex models.\n", | ||
| "Outside of the [beta](https://en.wikipedia.org/wiki/Beta_distribution)-[binomial](https://en.wikipedia.org/wiki/Binomial_distribution) model, the multivariate normal model is likely the most studied Bayesian model in history. `Pymc3` supports sampling from the [LKJ distribution](http://www.sciencedirect.com/science/article/pii/S0047259X09000876). The LKJ distribution represents the distribution on correlation matrices and is conjugate to the multivariate normal distribution. This post will show how to fit a simple multivariate normal model using `pymc3` with a normal-LKJ prior.\n", |
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Thanks @zaxtax. I agree that we should change the doc strings too. @junpenglao Wishart is pretty terrible (which form does not matter here): https://dahtah.wordpress.com/2012/03/07/why-an-inverse-wishart-prior-may-not-be-such-a-good-idea/ |
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Just to clarify, should I also update the doc strings on Wishart-Bartlett to nudge people to LKJ there as well? |
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Yes you should do that as well then. |
As the Wishart is highly discouraged now, including the Wishart-Bartlett form, we should change the documentation to not refer to it, and even perhaps talk more about the LKJ distribution.