maximum likelihood estimation of 5 parameters

Franco,
You can provide lower and upper bounds on the parameters if you use optim
with method="L-BFGS-B".
Hth, Ingmar

From: francogrex <francogrex at mail.com>
Date: Fri, 5 Jan 2007 04:54:50 -0800 (PST)
To: <r-help at stat.math.ethz.ch>
Subject: [R] maximum likelihood estimation of 5 parameters

Hi Guys, it would be great if you could help me with a MLE problem in R.

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? Thanks.

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