I need to evaluate the following internal:
$I=\int^{+\infty}_{-\infty}\dots\int^{+\infty}_{-\infty} f(x_,x_2,x_3\dots x_n) {1\over (\sqrt{2\pi})^N}e^{-{1\over2}x_1^2-{1\over2}x_2^2 \dots -{1\over2}x_n^2 } dx_1dx_2 \dots dx_n$
Where $f$ is quite complex and long story short I can't use standard Gaussian quadrature. So am I correct in thinking that I can generate $N$ Gaussian Random variables $g_{1i}$ and approximate $I$ as:
$I\sim{1\over N} \sum^N_{i=1}f(g_{1i}, g_{2i}, g_{3i} \dots)$
And ignore the limits? i.e no $({+\infty}--{\infty})$ out front like classic MC integration? Cheers Guys!