[R] empirical maximum likelihood estimation

Dominik Heinzmann dominik.heinzmann at math.unizh.ch
Thu Jan 19 13:01:16 CET 2006

Dear R-users


Given the following system of ordinary differential euqations

dM/dt = (-n)*M-h*M
dS/dt = n*M-h*S+u*R
dA/dt = h*S-q*A
dI/dt = q*A-p*I
dJ/dt = h*M-v*J

where M,S,A,I,J,R are state variables and n,h,u,q,p,v parameters.

I'm able to calculate the likelihood value based on the solutions 
M,S,A,I,J,R of the ODE's given the data, but without an explicit formula.

How can I now optimize the loglikelihood with respect to the parameter 
n,h,u,q,p,v? Is there any functions available in R for dealing with such 
empirical likelihood problems?

Thanks a lot for your support.

Dominik Heinzmann
Master of Science in Mathematics, EPFL
Ph.D. student in Biostatistics
Institute of Mathematics
University of Zurich

Winterthurerstrasse 190
CH-8057 Zürich
Office: Y36L90

E-Mail  : dominik.heinzmann at math.unizh.ch
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Homepage: http://www.math.unizh.ch/user/heinzmann

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