API for deterministic and stochastic surrogates.
Given data $((x_1, y_1), \ldots, (x_N, y_N))$ obtained by evaluating a function $y_i =
f(x_i)$ or sampling from a conditional probability density $p_{Y|X}(Y = y_i|X = x_i)$,
a deterministic surrogate is a function $s(x)$ (e.g. a radial basis function
interpolator) that
uses the data to approximate $f$ or some statistic of $p_{Y|X}$ (e.g. the mean),
whereas a stochastic surrogate is a stochastic process (e.g. a Gaussian process
approximation) that uses
the data to approximate $f$ or $p_{Y|X}$ and quantify the uncertainty of the
approximation.
