Re: Maximum Likelihood Estimation

*To*: mathgroup at christensen.cybernetics.net*Subject*: [mg1014] Re: Maximum Likelihood Estimation*From*: pehowland at taz.dra.hmg.gb (Paul E. Howland)*Date*: Wed, 10 May 1995 03:05:19 -0400*Organization*: Defence Research Agency

In article <3o9mtc$b92 at news0.cybernetics.net>, 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. -----------------------------------------------------------------------------