[R] multivariate integral with ADAPT when the parameter is close to boundary
Prof Brian Ripley
ripley at stats.ox.ac.uk
Sun Oct 19 07:51:04 CEST 2008
1) That integrand is a product, so you can do this a product of integrals,
and do those analytically.
2) Do you have any idea how extreme beta(0.005, 0.005) is? See the
comment in the help for integrate:
Like all numerical integration routines, these evaluate the
function on a finite set of points. If the function is
approximately constant (in particular, zero) over nearly all its
range it is possible that the result and error estimate may be
delta <- 1e-4
x <- seq(delta, 1-delta, delta)
plot(x, dbeta(x, 0.005, 0.005), type="l")
pbeta(0.9999, 0.005, 0.005) - pbeta(0.0001, 0.005, 0.005)
so 95% of the mass is outside the limits you set.
On Sun, 19 Oct 2008, Muhtar Osman wrote:
> Dear All,
> There is one problem I encountered when I used ADAPT to compute some
> 2-D integral w.r.t beta density.
> For example, when I try to run the following comments:
> int.fun2<-adapt(ndim=2,lo = c(0,0), up = c(1,1),functn = fun2,eps = 1e-4)
> It seems it will take very long time to run. Acturally, I stopped the
> program after it was running for like 20 minutes.
> I thought this might be due to the inclusion of the lower and upper in
> to the integral computation, so I tried to change the lower and upper
> int.fun2<-adapt(ndim=2,lo = c(0.0001,0.0001), up =
> c(0.9999,0.9999),functn = fun2,eps = 1e-4)
> It only took few seconds to run, but it gave me the wrong result:
> int.fun2= 0.00202210665273673, whereas the correct result should be int.fun2=1.
No, that's the correct answer for the problem you set.
> I guess the reason for this is beta(0.005,0.005) has very high density
> close to the boundary (theta=0).
> So even letting "lo = c(0.0001,0.0001)" will cause some loss of
> probability mass in the integral computation.
> I was wondering if anybody has encountered the similar problem before.
> Any comments are appreciated.
> Muhtar Osman
> Dept.of Stats
> R-help at r-project.org mailing list
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
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)
Oxford OX1 3TG, UK Fax: +44 1865 272595
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