[R] bivariate vector numerical integration with infinite range

[Hans W Borchers]

baptiste auguie <baptiste.auguie <at> googlemail.com> writes:

> 
> Thanks, adaptIntegrate() seems perfectly suited, I'll just need to
> figure a transformation rule for the infinite limit. The suggestion of
> x->1/x does not seem to work here because it also transforms 0 into
> -infinity. I think exp(pi* sinh(x)) could be a better choice,
> according to Numerical Recipes.

Yes, that's one way.
But you can also split the integral in two parts, one from 0 to 1 and then
from 1 to Inf. The first one is a finite hypercube and the second can be
transformed with x --> 1/x into [0, 1].

I usually prefer the second approach for higher-dimensional applications
as the Jacobian appears to be simpler. In the literature you will find 
discussions on how far out the finite hypercube should reach for lowering
the absolute error.

Hans Werner

> Thanks,
> 
> baptiste
>