Gaussian Processes for quasars

Undergraduate researcher David Mykytyn and I decided to work through the Rasmussen & Williams book on Gaussian Processes, and complete our exploratory project on fitting time-domain multi-band data on quasars in SDSS Stripe 82 data. We have made up a crazy covariance function, which accounts for time lags, differences in amplitude, and different time-scales in different bands; we are not sure if we have a kernel that is permitted to exist by the rules of mathematics. (An acceptable kernel is one that can only make positive definite covariance matrices.) One amusing thing we learned is that the industry-leading way to determine whether a kernel is permitted is to test the hell out of it numerically; proofs are much, much harder.

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