An illustration of a simple hierarchical GP. Top: the prior over the underlying function g
(t), with the mean μ(t)=0 shown as a heavy solid line, and the shaded area representing the variance (amplitude) of the function, controlled by the hyper-parameter α
. A single sample from the prior is shown as a narrow line, and the length-scale of the function, inversely controlled by the hyper-parameter γ
, is marked. Middle: three functions, representing three replicates are shown, along with samples conditioned on the sample shown in g
(t). The three replicates follow the trend of g
(t), but deviate independently by a small amount (variance α
) with a short length-scale, marked in the third replicate. Bottom: the covariance matrix used to generate the samples Σ
. Note the block-wise relationship to the replicates.