Re: Maximum Likelihood Estimation

• To: mathgroup at christensen.cybernetics.net
• Subject: [mg1135] Re: Maximum Likelihood Estimation
• From: pehowland at taz.dra.hmg.gb (Paul E. Howland)
• Date: Wed, 17 May 1995 03:19:17 -0400
• Organization: Defence Research Agency

```In article <3ocfkr\$o3o at news0.cybernetics.net>, Bill Harbaugh <harbaugh at students.wisc.edu> writes:
>One approach is to write out the likelihood function and then do a grid
>search, assuming it is too nasty for analytic methods.  I am doing this
>at the moment, and can tell you that mma is very, very, very slow for
>this purpose.  My bet is that you would be much happier with a package
>designed for this purpose, such as Gauss. On the otherhand, the symbolic
>abilities of mma can be useful for some problems

Rather than a grid search, why not try a "natural algorithm", such as
minimisation by simulated annealing or a genetic algorithm.  These are
basically empirical methods that randomly sample the error surface using an
algorithm analogous to something in nature (simulated annealing === cooling of
a crystaline substance, genetic algorithm === Darwin's ideas).  These will tend
to locate the global minimum of an error surface, unlike more traditional
search methods such as Steepest Descent, Gauss-Newton or Levenberg-Marquardt,
which tend to fall down the nearest local minimum. You can use the natural
algorithm to approximately locate the global minimum, and then use a
traditional method (as implemented in NonlinearFit and FindMinimum) to rapidly
converge on the least squares answer.

I've written my own genetic algorithm (GA) in Mathematica for this purpose,
and it is very effective - surprisingly so.  Since writing my GA, one has
appeared on MathSource - so it is now available to all (I haven't tried it
though).

Only use a grid search as a last resort - especially if you have a large number
of parameters.

Paul E Howland

Long Range Ground Radar Systems Section               tel. +44 (0)1684 895767
CSS2 Division, Room BY209                             fax. +44 (0)1684 896315
Defence Research Agency                           email: PEHOWLAND at DRA.HMG.GB
Malvern, Worcs, WR14 3PS, UK.
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```

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