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Science Forum Index » Statistics - Math Forum » maximum likelihood estimation of 5 parameters
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| franco |
 Posted: Fri Jan 05, 2007 9:23 am |
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Hi Guys, it would be great if you could help me with a MLE problem.
I am trying to evaluate the maximum likelihood estimates of theta =
(a1, b1, a2, b2, P) which defines a mixture of a Poisson distribution
and two gamma prior distributions (where the Poisson means have a gamma
distribution, actually 2 gammas and P is the mixing factor). The
likelihood function for theta is L(theta) = Pi,j{P f(Nij; a1, b1, Eij)
+ (1 - P) f(Nij; a2, b2, Eij),}
The maximum likelihood estimate of theta is the vector that maximizes
the above equation (the values of N and E are given). The authors of
the article I read say that the maximization involves an iterative
search in the five dimensional parameter space, where each iteration
involves computing log[L(theta)] and its first and second-order
derivatives. In test runs it is suggested that the maximization
typically takes between 5 and 15 iterations from the starting point
theta = (a1 = 0.2, b1 = 0.1, a2 = 2, b2 = 4, P = 1/3).
Now I have done maximization of a gamma-poisson mixture before (1
poisson, 1 gamma) successfully and I could determine correctly alpha
(a) and beta(a). But this one above is giving me ridiculously large
unusable values (for example P should not be above 1 and sometimes I
get values of 500!) or even negative values! I know the values I should
be obtaining with my samples shouldn't be far from the staring points.
Is there a way to help me solve this issue? I use R for statistical
analysis and I have tried several functions like MLE, optim etc. I am
not using a gradient (because I don't know how to make one, is it
because of that? Or are there constraints I need to set? Thanks. |
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