Efficiently estimating mean shift due to variability

This paper concerns the problem of calculating expectation shift due to variability which tends to occur whenever the function of a random variable is nonlinear and especially tends to occur in the neighborhood of a local maximum or minimum. The paper presents five theorems suggesting sampling points and formulae for estimating mean shift covering some of the most common cases of practical interest including multivariate normal distributions and uniform distributions as well as more general theorems covering all symmetric multivariate probability density functions.