the vector of random variables representing the properties of the previously evaluated NPMs, σ = [k(x, x 1 ), k(x, x 2 ), ..., k(x, x n )] the vector of the kernel between the unevaluted NPM and the previously evaluated NPMs, and Σ the kernel matrix for the previously evaluated NPMs with Σ i,j = k(x i , x j ) ∀i, j ∈ {1, 2, ..., n}. However, we have observations of the random variables in f, y = [y 1 , y 2 , • • • , y n ] . Conditioning the joint distribution in eqn. on the observations y, we arrive at the posterior distribution for the property f (x) of the unevaluated NPM, also Gaussian: