I’ll try to give examples of efficient gaussian process computation here, like the vec trick (Kronecker product trick), efficient toeliptz and circulant matrix computations, RTS smoothing and Kalman filtering using state space representations, and so on.
First of my experiments on audio modelling using gaussian processes. Here, I construct a GP that, when sampled, plays middle c the way a grand piano would.
… using Stan & HMC
A Minimal Working Example