Hi
yes that is very clear now.
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Yes, by scale parameter I meant the
std, might be quite challenging to sample from an uniform prior in the range 0.001 - 1000. -
I only played around with it a couple of times, but I believe you could use a Multivariate Normal with your noise matrix as covariance matrix. The lecture by Richard McElreath on Gaussian Processes is the most accessible resource I found so far on the subject.
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The same logic I suspect it also applies to samples, since they represent different points in time you might expect some form of temporal structure to be present. This would probably require a spatio-temporal model but this is something way out of my depth.