## Some more abuse of Gaussian processes …

Two arXivals today show us ways to mis-use or mis-apply Gaussian processes.  The first is another in this crazy series of papers trying to use GPs as extrapolators to estimate $H_0$ from $H(z)$ datapoints.  Yes, GPs can kind of extrapolate, but it’s really not their strength: as you get further and further from the domain of observed data you get the GP returning to the mean.  The only interesting thing is the rate at which it reverts, which is controlled by the GP kernel hyper-parameters: unfortunately, as we’ve discussed before, these are very difficult to estimate well for many types of experimental design.  As far as I can see from the scant details in this submission: the authors only look at how small the credible intervals on $H_0$ are from their GP fits, not at whether or not the true value from the model in the mocks is actually contained within them with any reasonable Frequentist coverage.  Interestingly, they do see that their credible intervals increase if they switch from a squared exponential kernel to various flavours of Matern, which recalls the observation from asymptotic theory that we should probably be using the Matern kernel if we actually want decent coverage.

The other GP paper today was presenting some ‘novel’ work that looks a lot like the Korean re-make version of an already published paper I was involved in via the COIN collaboration.  The idea there is to use spatial GPs as an interpolator to fill in gaps in irregularly sampled galaxy data (in our case it was IFU data) to construct a complete model ‘image’ (with uncertainties); plus maybe gain a little shrinkage at the observed locations.  Why I believe our version is a lot better is because we jointly fit a radial parametric function along with the GP, whereas today’s paper fits the radial term first and then separately fits the GP to the residuals.  There’s no computational need or theoretical justification to cut the fit at this point, especially if the errors in the first step are not going to be propagated coherently to the second.  Also, the first fit here is likely to give as sensible an estimate as most badly misspecified model fitting exercises; especially when you look at how irregular the ‘design’ of sampling locations is for some of these galaxies.