R help - Jan 2006 - empirical maximum likelihood estimation

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 Z??rich
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

Look at optim, or mle in package stats4.

There are a lot of similar problems addressed in R: few real-world 
likelihoods have `an explicit formula'.  One quite similar example is 
ARIMA fitting.

On Thu, 19 Jan 2006, Dominik Heinzmann wrote:
> 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 Z?rich
> 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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> PLEASE do read the posting guide!
http://www.R-project.org/posting-guide.html
>
-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595