# [R] empirical maximum likelihood estimation

From: Dominik Heinzmann <dominik.heinzmann_at_math.unizh.ch>
Date: Thu 19 Jan 2006 - 23:01:16 EST

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@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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