Gaussian Processes for astronomers

I spent my research time today (much of it on planes and trains) working on my seminar (to be given tomorrow) about Gaussian Processes. I am relying heavily on the approach advocated by Foreman-Mackey, which is to start with weighted least squares (and the Bayesian generalization), then show how a kernel function in the covariance matrix changes the story, and then show how the Gaussian Process is latent in this solution. Not ready! But Foreman-Mackey made me a bunch of great demonstration figures.