[R] empirical maximum likelihood estimation
Dominik Heinzmann
dominik.heinzmann at math.unizh.ch
Thu Jan 19 13:01:16 CET 2006
Dear R-users
Problem:
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
dR/dt=p*I+v*J-u*R
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 Zürich
Office: Y36L90
E-Mail : dominik.heinzmann at math.unizh.ch
Phone : +41-(0)44-635 5858
Fax : +41-(0)1-63 55705
Homepage: http://www.math.unizh.ch/user/heinzmann
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