[R] empirical maximum likelihood estimation

[Prof Brian Ripley]

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 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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-- 
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