# [R] empirical maximum likelihood estimation

Martin Maechler maechler at stat.math.ethz.ch
Thu Jan 19 17:59:19 CET 2006

```>>>>> "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
>>
>> ______________________________________________
>> R-help at stat.math.ethz.ch mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-help
>>

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______________________________________________
BDR> R-help at stat.math.ethz.ch mailing list
BDR> https://stat.ethz.ch/mailman/listinfo/r-help