FR tutorial on directional distributions

@OlaRonning would you be interested in collaborating on a tutorial on directional distributions, to host on https://pyro.ai/examples? I’d be happy to write up how to use VonMises, VonMises3D, ProjectedNormal, and ProjectedNormalReparam. It seems like also a nice place to promote your new toroidal distributions as well. One thing I could use help with is finding a nice public dataset to analyze. We could even write the tutorial in stages over multiple PRs, say building on @OlaRonning’s proposed example.

Tasks

• find one or two public datasets
• describe VonMises distribution
• describe VonMises3D distribution
• describe ProjectedNormal and ProjectedNormalReparam
• describe SineBivariateVonMises #2821
• describe SineSkewed #2826
• demonstrate MCMC inference
• demonstrate SVI inference with an AutoNormal and an AutoMultivariateNormal guide

[alexlyttle]

@OlaRonning

Regarding orbits, I think the angle tends not be important as we care more about the period and distance from the star.

I was wrong here… I think the “argument of periasteron” might be a good circular parameter example, which is involved in modelling the orbits of exoplanets. I can’t find an example of someone using Von Mises but it may well be appropriate here. I will first try recreating this tutorial from the exoplanet code (which uses public data) but in numpyro and reparameterize some of it to make use of a circular variable.

I’ll get back to you if there is progress on this, and may ask for help from exoplanet researcher friends!

[alexlyttle]

Hi @OlaRonning, I would love to help and I have been giving this some thought. At first I thought the inclination angle of stars may be a good example, but I don’t think the problem is circular and requires a different kind of reparameterization. In my own work, I have been using VonMises to model a phase parameter in a model (e.g b in y ~ sin(a*x + b)). The science behind this work a bit unusual, so it wouldn’t make a good tutorial. Regarding orbits, I think the angle tends not be important as we care more about the period and distance from the star.

That being said, I will have a deeper look into datasets, it would be cool to have an example from astronomy.