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Re: Maximum likelihood and Mathematica

snowrain wrote:

> I am doing MLE with Mathematica. When I put the parameters estimated from concentrated loglikelihood function into the gradient, the value is not close to zero. The command I used was "NMaximize". Does it only look for local maximum ?

The online documentation reads, "NMaximize always attempts to find a
global maximum of f subject to the constraints given. " Note that, "If
f and cons are linear, NMaximize can always find global maxima, over
both real and integer values. Otherwise, NMaximize may sometimes find
only a local maximum." Therefore, without more information about the
expressions and the options you are using, it is hard to diagnose what
the issue might be.

> When I estimate unconcentrated loglikelihood function, it shows error information that the loglikelihood is a complex number. There must be something wrong with the command that I am using since the concentrated and unconcentrated loglikehood functions should lead to the same estimate.
> I found there is a package "Global Optimization" by Mathematica. Do I have to purchase and use it to find global optimization? And, why do I have different answers from the two loglikelihood functions? How can I check the steps/process of how Mathematica estimates the parameters? Thanks a lot !

To check what NMaximize is doing during a computation, you can use
either one of the options EvaluationMonitor or StepMonitor. Note that
you can also control the accuracy and precision of the computation
(check AccuracyGoal, PrecisionGoal, WorkingPrecision, as well as
MaxIterations) and chose a specific algorithm (set the Method option
to "NelderMead", "DifferentialEvolution", "SimulatedAnnealing" or
"RandomSearch" for instance).


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