Hi,
Thanks for the tip, but it's still mysterious to me. Reading ?integrate did not
give me much hint as to what "relative accuracy" means in this context. I
looked at the source of integrate.c but it's still not clear to me how the
default value of rel.tol (10^-4 for me) is not enough to prevent a completely
wrong answer (the error is much larger than this).
Obviously, I'm worried now that I may not always choose a good value of
ref.tol, if picked arbitrarily without my understanding of what it means.
Thanks,
baptiste
On Sep 21, 2010, at 3:38 PM, Ravi Varadhan wrote:
> There is nothing mysterious. You need to increase the accuracy of
> quadrature by decreasing the error tolerance:
>
> # I scaled your function to a proper Gaussian density
> shiftedGauss <- function(x0=500){
> integrate(function(x) 1/sqrt(2*pi * 100^2) * exp(-(x-x0)^2/(2*100^2)), 0,
> Inf, rel.tol=1.e-07)$value }
>
> shift <- seq(500, 800, by=10)
> plot(shift, sapply(shift, shiftedGauss))
>
>
> Hope this helps,
> Ravi.
>
> -----Original Message-----
> From: r-help-boun...@r-project.org [mailto:r-help-boun...@r-project.org] On
> Behalf Of baptiste auguie
> Sent: Tuesday, September 21, 2010 8:38 AM
> To: r-help
> Subject: [R] puzzle with integrate over infinite range
>
> Dear list,
>
> I'm calculating the integral of a Gaussian function from 0 to
> infinity. I understand from ?integrate that it's usually better to
> specify Inf explicitly as a limit rather than an arbitrary large
> number, as in this case integrate() performs a trick to do the
> integration better.
>
> However, I do not understand the following, if I shift the Gauss
> function by some amount the integral should not be affected,
>
> shiftedGauss <- function(x0=500){
> integrate(function(x) exp(-(x-x0)^2/100^2), 0, Inf)$value
> }
>
> shift <- seq(500, 800, by=10)
> plot(shift, sapply(shift, shiftedGauss))
>
> Suddenly, just after 700, the value of the integral drops to nearly 0
> when it should be constant all the way. Any clue as to what's going on
> here? I guess it's suddenly missing the important part of the range
> where the integrand is non-zero, but how could this be overcome?
>
> Regards,
>
> baptiste
>
>
> sessionInfo()
> R version 2.11.1 (2010-05-31)
> x86_64-apple-darwin9.8.0
>
> locale:
> [1] en_GB.UTF-8/en_GB.UTF-8/C/C/en_GB.UTF-8/en_GB.UTF-8
>
> attached base packages:
> [1] stats graphics grDevices utils datasets methods base
>
> other attached packages:
> [1] inline_0.3.5 RcppArmadillo_0.2.6 Rcpp_0.8.6
> statmod_1.4.6
>
> loaded via a namespace (and not attached):
> [1] tools_2.11.1
>
> ______________________________________________
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> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
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>
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