How does one do MC for integrand which has poles?
$I=\int \frac{e^{-S(x)}}{f(x)}dx$
where $x$ would be multi-dimensional, and hence this is a multi-dimensional integral over coordinates such as $x_1,x_2,x_3$ and so on.
I want to do importance sampling. Suppose this function has poles at $x_i$, such that $f(x_i)=0$. How does one perform importance sampling on functions with poles? Generally, how does one perform MC sampling on integrand with pole(s)?