Random sampling-high dimensional model representation (RS-HDMR) with nonuniformly distributed variables: Application to an integrated multimedia/multipathway exposure and dose model for trichloroethylene

The high dimensional model representation (HDMR) technique is a procedure for representing high dimensional functions efficiently. A practical form of the technique, random sampling-high dimensional model representation (RS-HDMR), is based on randomly sampling the overall function. In reality, the samples are often obtained according to some probability density functions (pdfs). This paper extends our previous RS HDMR work with uniformly distributed random samples to those with a nonuniform distribution and treats uniform sampling as a special case. Weighted orthonormal polynomial expansions are introduced to approximate the RS-HDMR component functions. Different pdfs give special formulas for the weighted orthonormal polynomials. However, the structure of the formulas for the RS-HDMR component functions represented by the Monte Carlo integration approximation are the same for all pdfs. The correlation method to reduce the variance of the Monte Carlo integration and the method to represent the high order terms by lower order terms in uniform RS-HDMR can also be used for nonuniform RS-HDMR. The theoretical basis of nonuniform RS-HDMR is provided, and an application is presented to an integrated environmental exposure and dose model for trichloroethylene.