[R] Analytical Optimization (Stat question)

francogrex
Wed, 16 Jan 2008 11:06:37 -0000

Dear Experts, this is more a general stat question, I tried to ask in other
places but had no luck with answers (expect one that suggested numerical
instead of analytical optimization):
The likelihood below is a mixture of two negative binomial
distributions:
P*f(n;x1,x2,E) + (1-P)*f(n;x3,x4,E)
N and E are vectors of same length. I would like to find the fist
derivatives with respect to x1,x2,x3,x4 and P (so that I can set them
to zero and calculate a bayesian MLE by iterations according to  David
Draper's
"Bayesian Modeling, Inference and Prediction").
Does anyone have a "quick and dirty" way? To avoid drawning in rather
complicated math...
Here's the transcription of the likelihood in S language:
P*exp((lgamma(x1+N)))-(((lgamma(x1)+lfactorial(N))+log((1+(E/
x2))^x1)+log((1+(x2/E))^N)))+
(1-P)*exp((lgamma(x3+N)))-(((lgamma(x3)+lfactorial(N))+log((1+(E/
x4))^x3)+log((1+(x4/E))^N)))
--
View this message in context:
http://www.nabble.com/Analytical-Optimization-%28Stat-question%29-tp14878234p14878234.html
Sent from the R help mailing list archive at Nabble.com.