[R] High Dim Gauss Hermite Approximation

Jie
2012-08-01T18:27:03Z

Dear All,

I am writing code of Gauss Hermite Approximation for 2-d case.
Suppose I want to calculate the integral \int g(b)*exp(-b' W b) db, where b
is a 2 by 1 vector, W is a 2 by 2 positive definite matrix,
In order to get the basic form, I need decompose W = L' L, and define
x=L*b, i.e. b= L^(-1) x, where x are the pre-determined nodes. But since
this L is only unique up to a orthogonal transformation, I noticed that
chosing different L's, my result are slightly different. Should I expect
that if I use more node, essential I will get closer estimations?
Does Adpative Gauss hermite Version improve much?

If I post to a wrong place, please let me know. Thank you.

Best wishes,
Jie

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