Check out this cool Gaussian Process Simulation! Gaussian processes, or GPs, are an integral part of Bayesian optimization and adaptive experiment design. I came across the linked simulation at the start of my SURF when I was first trying to understand GPs, and was reminded of it today for a funny reason. A GP is basically an infinite multivariate distribution of functions. When learning about GPs, 2D plots are usually used to demonstrate the concept and often show functions sampled from the GP, like this or this. Because of the way they’re depicted, I figured sampling a function from a GP must be relatively simple, as that seems like a practical use for having such a distribution of functions. As it turns out, the 2D case is quite misleading–sampling from a GP is tractable because you’ve only a 2 by 2 covariance matrix and because one can simply discretize the function on the 2-D domain and construct a joint distribution across those discrete points. In higher dimensions, this is much less trivial, which is quite unfortunate for my project… Anyhow, the simulation is still fun to play with!