[R] Multivariate integration with infinite limits

[Prof Brian Ripley]

On Sat, 10 Nov 2007, Uwe Ligges wrote:

>
>
> Paul Smith wrote:
>> Dear All,
>>
>> Can R perform multivariate integration with infinite limits of integration?
>
> No, R does numerical (not symbolical) calculations, hence it can never
> perform integration (not even univariate) with infinite limits.

Not really true, as I managed to implement it in integrate().  There is 
nothing to stop a numerical integration routine working on an infinite 
interval if some assumptions are made about the rate of decay of the 
integrand at infinity: several of the classical numerical quadrature 
formulae (e.g. Gauss-Hermite) are for infinite intervals.  (You can think 
of these as making a particular pre-assigned transformation to e.g. [-1, 
1].)

dqagi is adaptive, but at the heart is a Gauss-Kronrod rule done on a 
half-infinite interval.


-- 
Brian D. Ripley,                  ripley at 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)
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