However, when the noise scale is either variable (but known) or can be modeled with a relatively simple (e.g., parametric) model, there may be some benefit to the added model complexity. Here you could include the parameters of the noise model into the model hyperparameters and proceed following the discussion in chapter 4. In doing so, I would be careful to ensure that the data actually support the heteroskedastic noise hypothesis.
Another approach that might be useful in some contexts is a heavy-tailed noise model such as Student-t errors (§§ 2.8, 11.9, 11.11).
So for example, rather than simulate an entire month in one shot, I'll simulate a day 30 times and therefore have a decent estimate of the noise for that result and be able to clearly distinguish the noise from the covariance of the Gaussian process.
The noise in these simulations can vary dramatically in parameter space (easily 10-100x), so it seems like it would be important to model.
I believe that modeling the noise directly using a 2nd Gaussian Process [1] could help, but I haven't gotten reliable results. I was hoping this topic would be addressed in the book, but don't see it.
The private key part is secret of course, never shared (that's where the analogy above breaks) but the public part is fine and desirable for everyone to have access to - that's how they verify that you signed something with your private key, how they encrypt a secret message to you.
With PoW you don't care about the software code. The rules are dominated by the PoW because it literally proves to you which is the chain where most people are interested in, because literally no single entity could burn that much electricity.
With PoS on the other hand you kind of need these checkpoints in the actual software and then you have to activate this entire new trust model where you have to trust the client code, and where it came from etc. I could literally come up with an entire fake chain on my computer and present it to you and without client-checkpoints there would be no way for you to not accept my chain compared to your current one.
With PoW I don't have to trust anything. If the majority next year decides to change the rules, so be it. The majority has spoken.