[R] Problem with numerical integration and optimization with BFGS
Ben Bolker
bolker at zoo.ufl.edu
Fri May 25 00:44:19 CEST 2007
Deepankar Basu <basu.15 <at> osu.edu> writes:
>
>
> For my model, the likelihood function for each observation is the sum of
> three integrals. The integrand in each of these integrals is of the
> following form:
>
> A*exp(B+C*x-D*x^2)
>
(where D is positive)
Being very lazy, I tried Mathematica's online integrator
(http://integrals.wolfram.com/index.jsp), which says that
2
Integrate[Exp[b + c x - d x ], x] ==
2
b + c /(4 d) -c + 2 d x
E Sqrt[Pi] Erf[----------]
2 Sqrt[d]
--------------------------------------
2 Sqrt[d]
R knows "Erf" (the error function)
as pnorm -- can you use this to avoid numerical
integration entirely ??
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