[R] Gaussian Adaptive Quadrature

[Douglas Bates]

On 3/21/07, Doran, Harold <HDoran at air.org> wrote:
> The function integrate() uses AGQ. There are other functions for
> gaussian quadrature in the statmod() package that I really like.

I think that integrate does adaptive quadrature but not adaptive
Gaussian quadrature (which probably should have been called adaptive
Gauss-Hermite quadrature to be more specific).  In the first case the
"adaptive" refers to a choice of mesh size.  In the second case one is
integrating a function that is close to a multivariate Gaussian
density by first finding the conditional optimum of the integrand and
using a quadratic approximation to the log-integrand to establish the
location of the Gauss-Hermite quadrature points.

The Laplace approximation to the log-likelihood for a generalized
linear mixed model is a 1-point adaptive Gauss-Hermite quadrature
evaluation.

>
> > -----Original Message-----
> > From: r-help-bounces at stat.math.ethz.ch
> > [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Caio
> > Lucidius Naberezny Azevedo
> > Sent: Wednesday, March 21, 2007 5:55 AM
> > To: Help mailing list - R
> > Subject: [R] Gaussian Adaptive Quadrature
> >
> > Hi all,
> >
> >   Does anybody know any function that performs gaussian
> > adapative quadrature integration of univariate functions?
> >
> >   Thanks in advance,
> >
> >   Regards,
> >
> > Caio
> >
> >  __________________________________________________
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