ADAPTIVE QUADRATURE WEIGHTS AND NODES

On Fri, May 8, 2009 at 7:07 AM, Boikanyo Makubate

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.)

Beyond what Doug said, if you have a specific R function that does 
adaptive quadrature, you could read the code for that function.  You can 
get that without comments by typing the function name at a commands 
prompt.  To get the source code with comments, you can download the 
appropriate source code in *.tar.gz format from your favorite CRAN 
mirror.  If the function you want is in the base system, click "R 
Sources -> R-2.9.0.tar.gz" from your favorite CRAN mirror.  For a 
contributed packages, click "Packages" two lines below "R Sources". 


      The following will search help files for "adaptive quadrature": 

library(RSiteSearch)
aq <- RSiteSearch.function('adaptive quadrature')
summary(aq)
HTML(aq)

     
      Hope this helps. 
      Spencer Graves

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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