[Bug-gsl] Re: [Help-gsl] Negative chi squared value in MC Vegas

[Brian Gough]

At Tue, 7 Oct 2008 09:55:06 -0600 (MDT),
L. A. Pritchett-Sheats wrote:
> I'm writing an integration package which calculates N dimensional
> integrals on infinite intervals using the GSL Monte Carlo functions. I'm
> using tan(pi/2 x) to transform the integral to the (0,1) domain. For
> different functions, I've seen negative values for the chi/dof values.
> This is a reproducer integrating a gaussian on (0,+inf) that follows the
> sample code found in the GSL manual where I've seen this problem on both a
> Mac ( 10.4.11, Intel ) and a Linux machine (AMD Operton 86x_64). Although
> the values differ on the two machines, at least 2-3 calls in the loop will
> return a negative value for chi/dof.

This will be fixed in the next release.  The original vegas code
computed the chi-squared using a <x^2>-<x>^2 type formula, so it
suffered loss of precision when the relative errors were below O(1e-8)
Thanks for the bug report.

-- 
Brian Gough

GNU Scientific Library -
http://www.gnu.org/software/gsl/