Hello, I've been learning how to use GPFlow recently and it's fantastic! The GPR with Varying Output Noise Demo 3 example is particularly helpful for my use case.

The explanation for this Demo 3 is very clear:

"The shaded gray area is the confidence interval of f. We use vertical lack lines to indicate the confidence interval of the Y mean. [...] You may notice that the data points fall outside our confidence interval. Again, this is because the confidence interval is for the mean of Y, and not the Y points themselves."

My silly question is: If I did indeed want to retrieve the confidence interval of the Y points themselves, could this involve doing a Bayesian fit to estimate the variance for each distribution (i.e., the distributions at the each x-value) independently?
Although, I believe this analysis would give me a credible interval instead of a confidence interval but nevertheless, I'm just trying to understand this "Y points themselves" piece a bit more.

Thanks for any help you can provide!