Before revision: The computation of probability density functions (PDF) using approximate maps (surrogate models) is a building block in such diverse fields as forward uncertainty quantification (UQ), sampling algorithms, learning, and inverse problems. In these settings, the probability measure of interest is induced by an unknown map from a known probability space to the real line, i. e., the measure of interest is a pushforward of another known measure.
After revision: The computation of probability density functions (PDF) using approximate maps (surrogate models) is a building block in computational probability. We consider forward problems in uncertainty quantification: the inputs or the parameters of an otherwise deterministic model are random with a known distribution. The scalar quantity of interest is a pushforward of another known measure.