From: Prof Brian Ripley <ripley_at_stats.ox.ac.uk>

Date: Thu 10 Mar 2005 - 18:56:34 EST

}

Date: Thu 10 Mar 2005 - 18:56:34 EST

Nils,

For 2D, see package 'adapt' on CRAN. e.g.

adapt(2, c(0,0), c(1,1), functn=function(x) sin(prod(x))*exp(x[1]-x[2]))

Package `adapt' will do larger numbers of dimensions, but numerical quadrature is often no more effective than Monte-Carlo methods in more than a few dimensions. For very smooth functions, quasi-random numbers can help.

A good reference aimed at statisticians is

@Book{Evans.Swartz.00,

author = {Michael Evans and Tim Swartz}, title = {Approximating Integrals via Monte Carlo and Deterministic Methods}, publisher = {Oxford University Press}, year = 2000, address = {Oxford}, ISBN = "0-19-850278-8",

}

BTW, we are not good are predicting to 2014, but fairly good at the present. In this case I could not guess a good search term on http://search.r-project.org, but it often gets you there. It has a `complete' list of packages, as does CRAN, and searching those pages for `integrate' works.

Brian

On Thu, 10 Mar 2005, Nils-at-Duke Lid Hjort wrote:

> I find the one-dimensional "integrate" very helpful,

*> but often enough I stumble into problems that require
**> two (or more)-dimensional integrals. I suppose there
**> are no R functions that can do this for me, "directly"?
**>
**> The ideal thing would be to be able to define say
**> f <- function(x)
**> {
**> x1 <- x[1]
**> x2 <- x[2]
**> sin(x1*x2)*exp(x1-x2)
**> }
**> and then write say
**> integrate(f, xlim=c(0,1), ylim=c(0,1)) .
**>
**> (a) No such thing exists, as of today, right?
**> (b) There *are* general numerical routines "out there"
**> for doing such things, right? (Importance sampling
**> or adaptive important sampling would often do the
**> job, but it would be difficult to find something that
**> "always" works -- at least in higher dimension?
**> Also, iterated one-dimensional integrations could
**> be attempted, but I find that messy, also because
**> things lose the g(many) = many(g) property, and
**> then R refuses to integrate g.)
**> (c) Will a thing like the above exist in R before
**> the Tromsoe Olympics in 2014? For which dimensions?
**> Nils Lid Hjort
**> [Professor of statistics at Oslo, but currently at Duke]
*

-- Brian D. Ripley, ripley@stats.ox.ac.uk Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/ University of Oxford, Tel: +44 1865 272861 (self) 1 South Parks Road, +44 1865 272866 (PA) Oxford OX1 3TG, UK Fax: +44 1865 272595 ______________________________________________ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.htmlReceived on Thu Mar 10 19:19:52 2005

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