More and better tutorials

[pscicluna]

In the review (https://github.com/ICSM/pgmuvi/issues/45), @baptklein requested that we improve the tutorials in a few different ways:

In both tutorials, we are modelling a simple sine-wave curve. I reckon that this tests is essential to make the code user friendly, and I am very happy that the authors provided this test. However, after reading the papers associated with this submission, I believe that this code is designed to do more than a sine-wave fit. Could the authors provide me (or the user) with the following applications: (1) A relevantly-thought multi-wavelength case (which is what the code has been designed for) (2) A non-strictly-periodic signal (e.g. quasi-periodic). It would be also interesting to provide a test with highly uneven sampling to test the capacity of the code to find the right periodicities for realistic ground-based observations. (3) I would also suggest to add an example where the GP is coupled with a deterministic model (i.e. a non-zero mean function). For example, it could be a linear trend or a sine-wave curve. GPs are often coupled with a deterministic mean function where physical parameters can be assessed. (4) Finally, could I easily use the pgmuvi to generate mock data sets from a GP with a given covariance kernel? If yes, could the authors explain how.

We can discuss how to work on these in this issue.

I think most of these are quite easy to implement -

• 1 and 2 just require changing how the test dataset is generated. If we wanted, we could take some real datasets for 2, since some of the interesting astronomical sources are quasi-periodic (like semi-regular LPVs)
• 4 is also quite straightforward (gpytorch does this easily), but does require some minor updates to pgmuvi to make it fit the style of the rest of the code.
• everything exists for 3 for a linear mean function, but not for a sine function or anything more complicated.

Other comments more than welcome!