Hello,
Let me try to clarify the reasons why someone would
try to construct maximum likelihood estimators using
Maxima.
Yes, R and some other packages are very useful for
solving curve fitting -- once the solution is well
established and reduced to a certain fixed algorithm.
The point of using Maxima is to construct estimators
for problems which are not yet well-known. The
linear regression problem is just a practice problem.
I can't speak for Ross Clement, but my own interest
in these problems revolves around inference in
probabilistic models. Inferences can very generally
be phrased in terms of integrations. Whether or not
the integrations can be carried out depends on the
structure of the model; there could be an algorithm
which attempts a symbolic integration and falls back
on numerical methods if that fails.
Likewise, parameter fitting in such models depends on
the exact structure of the model. If nothing else, it
would be very convenient to construct the gradient of the
likelihood and use that as the basis for a numerical
fitting algorithm.
The point is to move some or all of the burden of
inference and parameter fitting to an automatic program;
the goal is to spend more time thinking about
interesting problems.
For what it's worth,
Robert Dodier
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