[R] empirical maximum likelihood estimation

[Martin Maechler]

>>>>> "BDR" == Prof Brian Ripley <ripley at stats.ox.ac.uk>
>>>>>     on Thu, 19 Jan 2006 12:38:12 +0000 (GMT) writes:

    BDR> Look at optim, or mle in package stats4.
    BDR> There are a lot of similar problems addressed in R: few real-world 
    BDR> likelihoods have `an explicit formula'.  One quite similar example is 
    BDR> ARIMA fitting.

Further note the package   'nlmeODE'
which efficiently addresses a problem very similar to yours.

Martin Maechler, ETH Zurich

    BDR> 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ürich
    >> 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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    >> 

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