[R] ADAPTIVE QUADRATURE WEIGHTS AND NODES
Douglas Bates
bates at stat.wisc.edu
Fri May 8 19:07:05 CEST 2009
On Fri, May 8, 2009 at 7:07 AM, Boikanyo Makubate
<boikanyo at stats.gla.ac.uk> wrote:
> Can anyone help me on how to get the nodes and weights of the adaptive quadrature
> using R.
You need to be more specific about which quadrature formula. I'm
guessing that you probably have Gauss-Hermite quadrature in mind
because it is used when a density is approximated by a Gaussian
density (the "adaptive" modifier refers to a process where the
conditional mode and conditional variance are determined, given values
of parameters). In that case you could start at
http://en.wikipedia.org/wiki/Gauss-Hermite_Quadrature
for the theory.
There is C code in the lme4 package to compute the nodes and weights
for Gauss-Hermite quadrature but we haven't written a public interface
to it. You can try, for example
> library(lme4)
> .Call("lme4_ghq", 7)
[[1]]
[1] 2.6519614 1.6735516 0.8162879 0.0000000 -0.8162879 -1.6735516 -2.6519614
[[2]]
[1] 0.0009717812 0.0545155828 0.4256072526 0.8102646176 0.4256072526
[6] 0.0545155828 0.0009717812
to get the nodes and the weights for a 7-point Gauss-Hermite
quadrature. (There are two versions of the Hermite polynomials, the
physicist's version where the kernel is exp(-x^2) and the
probabilist's version where the kernel is exp(-(x^2)/2). I'm pretty
sure these are from the physicist's version.)
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