We propose a stochastic framework based on sensitivity analysist (SA) methods to quantify the key-input parameters influencing the Young's modulus of polymer (epoxy) clay nanocomposites (PCNs). The input parameters include the clay volume fraction, clay aspect ratio, clay curvature, clay stiffness and epoxy stiffness. All stochastic methods predict that the key parameters for the Young's modulus are the epoxy stiffness followed by the clay volume fraction. On the other hand, the clay aspect ratio, clay curvature and the clay stiffness have an insignificant effect on the Young's modulus of PCNs. Besides the results on the sensitivity of the input parameters, this work includes a comparative study of a series of stochastic methods to predict mechanical properties of PCNs with respect to their performance.