Today Soledad Villar (JHU) and I completed a problem I've had open for literally years (I think I first worked on it in AstroHackWeek 2017): Does a linear fit become a Gaussian process when the number of components (parameters) goes to infinity? The answer is yes! But you have to choose your features very carefully, and take the limit (to infinite features) sensibly. But if you meet those conditions it works, and the kernel function for the GP becomes a Fourier transform of the squares of the amplitudes of the features. That is, the kernel function in real space is the Fourier transform of the power spectrum in fourier space. There are many details I don't yet understand, but we got it working both theoretically (on paper) and numerically (on the computer).
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