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Re: Maximum Likelihood Estimation

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  • Subject: [mg1014] Re: Maximum Likelihood Estimation
  • From: pehowland at (Paul E. Howland)
  • Date: Wed, 10 May 1995 03:05:19 -0400
  • Organization: Defence Research Agency

In article <3o9mtc$b92 at>, Steve Faraone <72233.540 at CompuServe.COM> writes:
>Does anyone know of a routine in Mathematica that uses numerical 
>iteration to do maximum likelihood estimation of statistical models?
>Steve Faraone

It all depends on what you mean by "Maximum Likelihood".  If your errors are
Gaussian distributed then a least squares fit will be "maximum likelihood", in
which case you could use the standard NonlinearFit package, which uses a
Levenberg-Marquardt algorithm to minimise the least squares function 

	J = Transpose[(h-z[x])](h-z[x])

where h is a vector of your data
      z is your model
      x are the parameters of your model

NonlinearFit will return the values of x that minimise the least squares
diifference between your data and your statistical model.

If your errors have a distribution other than Gaussian, then a least squares
estimate will not necessarily be the Maximum Likelihood estimate, in which case
you will have to derive the likelihood function yourself, and try to find the
parameters which maximise your likelihood function.  You can use the built in
function FindMinimum to do this.

Hope this helps.

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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