Before revision:  We present an alternate statistical method for estimating an n-dimensional integral that is suited even for non-convex domains and scales as O(n) in the samples required, given any distribution of extents of the arbitrary domain and the allowed tolerance in relative error. This results due to the possible decomposition of an arbitrary n-volume into an integral of statistically weighted volumes of n-spheres  .
After revision:  We present an alternate statistical method for estimating an n-dimensional volumes, that is agnostic to the convexity and roughness of the body. It results due to the possible decomposition of an arbitrary n-volume into an integral of statistically weighted volumes of n-spheres .