We extend the classical empirical interpolation method [M. Barrault, Y. Maday, N.C.
Nguyen and A.T. Patera, An empirical interpolation method: application to efficient
reduced-basis discretization of partial differential equations. Compt. Rend. Math.
Anal. Num. 339 (2004) 667–672] to a weighted empirical
interpolation method in order to approximate nonlinear parametric functions with weighted
parameters, e.g. random variables obeying various probability
distributions. A priori convergence analysis is provided for the proposed
method and the error bound by Kolmogorov N-width is improved from the recent work [Y.
Maday, N.C. Nguyen, A.T. Patera and G.S.H. Pau, A general, multipurpose interpolation
procedure: the magic points. Commun. Pure Appl. Anal. 8
(2009) 383–404]. We apply our method to geometric Brownian motion, exponential
Karhunen–Loève expansion and reduced basis approximation of non-affine stochastic elliptic
equations. We demonstrate its improved accuracy and efficiency over the empirical
interpolation method, as well as sparse grid stochastic collocation method.