Modelling the variance in linear regression (heteroscedasiticy)

[mohelm]

Hi,

first many thanks for the fantastic project. It makes it really easy to start with Baysian inference!

I have a quick question: is it possible to provide a model for the variance parameter in linear regression? In other words, can you estimate models that allow for heteroscedasticity?

[tomicapretto]

Hi @mohelm

It's not possible at the moment, but it is something I would like to add. There are a couple of issues more urgent than this one, so this is not happening very soon. But I also expect this not to take too long. I'll post any updates here.

[mohelm]

Hey @tomicapretto , thanks for the quick reply. Great to hear that you are interested in this.

So, currently, this would have to be done in pymc3 (for instance) directly, right? Is there a chance you have a reference for this - I only found this so far.

[tomicapretto]

@mohelm I have a couple of examples :)

You could consult this great post by Austin Rochford https://austinrochford.com/posts/2021-08-11-splines-hetero.html and this notebook https://github.com/bambinos/unfinished-ideas/blob/main/heteroskedastic_spline.ipynb in our unfinished ideas repository.

Note that both work with splines. But it should be enough to understand how to apply it to other linear models.

[aloctavodia]

In Section 4.2 of https://bayesiancomputationbook.com/markdown/chp_04.html you will find another example.

[mohelm]

fantastic, thank you both.