Notebook with linear regression (Gauss-Linear model)

[tommyod]

• Added the Gauss-Linear case in a notebook.
• I believe this is a nice notebook to experiment with, since the Gauss-Linear case is what ESMDA is based on.
• The notebook allows the user to easy experiment with (1) number of ensemble members, (2) number of parameters, (3) number of observations and (4) strength of the prior.

[Blunde1]

I read through the notebook, and it looks brilliant. Great job 🚀
I had one small wish, but I can write that in an issue for later:

• if we sample from a prior more aligned with the linear model, we should expect better posterior results than the uninformed maximum likelihood, right?

Anyway, probably good to just get this in ASAP without adding anything.

[tommyod]

if we sample from a prior more aligned with the linear model, we should expect better posterior results than the uninformed maximum likelihood, right?

Yes. For instance, if we sample a tight prior around what we know to be true values, we should beat the ML estimate.

Anyway, probably good to just get this in ASAP without adding anything.

Agree. I'll merge now. Feel free to do a pass through it after it's merged and update if you wish to.