The High Dimensional Model Representation (HDMR) technique decomposes an n-variate function f ( x) into a finite hierarchical expansion of component functions in terms of the input variables x = ( x, x, . . . , x). The uniqueness of the HDMR component functions is crucial for performing global sensitivity analysis and other applications. When x, x, . . . , x are independent variables, the HDMR component functions are uniquely defined under a specific so called vanishing condition. A new formulation for the HDMR component functions is presented including cases when x contains correlated variables. Under a relaxed vanishing condition, a general formulation for the component functions is derived providing a unique HDMR decomposition of f ( x) for independent and/or correlated variables. The component functions with independent variables are special limiting cases of the general formulation. A novel numerical method is developed to efficiently and accurately determine the component functions. Thus, a unified framework for the HDMR decomposition of an n-variate function f ( x) with independent and/or correlated variables is established. A simple three variable model with a correlated normal distribution of the variables is used to illustrate this new treatment. [ABSTRACT FROM AUTHOR]