[R] multidimensional integration not over a multidimensionalrectangle

[Spencer Graves]

	  The (non)respoonse that I've seen to your question combined with my 
own search suggests that R does not yet have a multidimensional 
numerical integration function of the generality you desire.

	  Would you care to tell us more about the problem you are trying to 
solve?  For example, if it can be parameterized as an integral over R^k 
where the integrand is unimodal, you could approximate the integrand 
with a parabolic then do Monte Carlo from the obvious approximation of 
that integral by a multivariate normal.  For each selected point, you 
compute the ratio of your integrand to the approximating normal density. 
  Then compute mean and standard deviation of these ratios.  The mean is 
the evaluation of the integral, and stdev/N estimates the error.  For 
more information, see any good reference on "importance sampling", e.g.:

	  Evans and Swartz (2000) Approximating Integral via Monte Carlo and 
Deterministic Methods (Oxford).

	  hope this helps.
	  spencer graves

Lynette Sun wrote:

> Hi,
> 
> anyone knows about any functions in R can get multidimensional integration
> not over a multidimensional rectangle (not adapt).
> 
> For example, I tried the following function f(x,n)=x^n/n!
> 
> phi.fun<-function(x,n)
> { if (n==1) {
> 	x
> 	}else{
> 		integrate(phi.fun, lower=0, upper=x, n=n-1)$value
> 		}
> }
> 
> I could get f(4,2)=4^2/2!=8, but failed in f(4,3)=4^3/3! Thanks
> 
> Best,
> Lynette
> 
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