My comments on the manuscript

[dfm]

I will continue to edit this as I go through the paper.

Abstract:

• [x] Most people wouldn't agree that GPs are used for their "computational efficiency" :D
• [x] I don't agree with the statement that physically motivated GPs haven't been used to good effect. There are plenty of solid examples of measuring rotation periods and asteroseismic parameters using GPs. I think the better statement is that the specific things that you want to measure are hard, regardless of method. I now explicitly and exclusively refer to "star spot" variability. Let me know if that's better.
• [x] "ridden by degeneracies"? Is "ridden" the right word?
• [x] "of the Gaussian process that best describes" -> "of an effective GP model to describe"
• [x] "when employed in an inference setting"

Introduction

• [x] I think this section should be re-structured to lead with the astronomical application rather than an introduction to GPs. In fact, I think that some of the pedagogy could be removed or moved to another section/appendix. Instead, start with why it's interesting to measure these spot properties and why it's hard.
• [x] I think the word "extremely" is being overused: it is neither "extremely" easy or efficient to work with GPs. Perhaps "well-defined"? Lol. Ctrl+F yields 27 instances of "extremely"! I should look at a word cloud for this paper...
• [x] Eq 3-6, I'm not sure that it's necessary to include all these example kernels here. I want to keep them because I reference them later (in the temporal GP discussion of the Extensions section) and I need to motivate how many of their hyperparameters are not interpretable.
• [x] There has been some work on empirically interpreting the parameters of these standard GP kernels and their relationship to physical quantities by fitting simulated data: e.g. https://arxiv.org/abs/2012.01862 and references therein. These efforts should be cited!

[dfm]

Just a reminder from our conversation with Hogg and Winn:

It might be worth brainstorming a little about the order of presentation, and perhaps even breaking this into two papers.

I'm still going through the draft and I think this is really important because I'm don't find the current motivation very compelling. I think leading with a more thorough discussion of ensemble models, the null space, and maybe even a demo of the results before the GP stuff would be better.

[rodluger]

Done. Paper length increased to 103 pages as requested.

[dfm]

More comments from another read through:

• Move calibration tests to appendix
• Move implementation discussion to parallel JOSS paper
• What about moving the discussion of degeneracies, null space, limb darkening, and the benefits of ensembles to a separate paper
• I think it could be worth emphasizing more that even if you don't care about the stellar surface, you might still want to use this model.