Gaussian Process kernel zoo

What you are seeing: a Gaussian Process is a probability distribution over functions: pick any kernel $k(x, x')$ and the GP says "any function I might draw has covariance given by $k$". Top panel: five random functions drawn from the prior (no observations) at the current kernel. Bottom panel: five draws from the posterior after conditioning on three observed points (yellow dots) with noise $\sigma_n$.

Five kernels: RBF (squared exponential, very smooth), Matern 3/2 (continuous, 1-time-differentiable), Matern 5/2 (twice differentiable), periodic (exact repetition with period $p$), linear (Bayesian linear regression in kernel disguise). The blue band is mean $\pm$ 2 sigma. Click on the plot to add an observation.