A NOTE ON GAUSS-HERMITE QUADRATURE

For Gauss-Hermite quadrature, we consider a systematic method for tran sforming the variable of integration so that the integrand is sampled in an appropriate region. The effectiveness of the quadrature then dep ends on the ratio of the integrand to some Gaussian density being a sm ooth function, well approximated by a low-order polynomial. It is poin ted out that, in this approach, order one Gauss-Hermite quadrature bec omes the Laplace approximation. Thus the quadrature as implemented her e can be thought of as a higher-order Laplace approximation.