to clarify: by "if you knew that LL(psi+eps) were well approximated
by LL(psi), for the values of eps used to evaluate numerical
derivatives of LL. "
I mean the derivatives of LL(psi+eps) are close to the derivatives of LL(psi),
and perhaps you would want the hessian to be close as well.
albyn
Quoting Albyn Jones <jo...@reed.edu>:
Hi Kristian
The obvious approach is to treat it like any other MLE problem: evaluation
of the log-likelihood is done as often as necessary for the
optimizer you are using: eg a call to optim(psi,LL,...) where
LL(psi) evaluates the log likelihood at psi. There may be
computational shortcuts that would work if you knew that LL(psi+eps)
were well approximated by LL(psi), for the values of eps used to
evaluate numerical derivatives of LL. Of course, then you might
need to write your own custom optimizer.
albyn
Quoting Kristian Lind <kristian.langgaard.l...@gmail.com>:
Hi there,
I'm trying to solve a ML problem where the likelihood function is a function
of two numerical procedures and I'm having some problems figuring out how to
do this.
The log-likelihood function is of the form L(c,psi) = 1/T sum [log (f(c,
psi)) - log(g(c,psi))], where c is a 2xT matrix of data and psi is the
parameter vector. f(c, psi) is the transition density which can be
approximated. The problem is that in order to approximate this we need to
first numerically solve 3 ODEs. Second, numerically solve 2 non-linear
equations in two unknowns wrt the data. The g(c,psi) function is known, but
dependent on the numerical solutions.
I have solved the ODEs using the deSolve package and the 2 non-linear
equations using the BB package, but the results are dependent on the
parameters.
How can I write a program that will maximise this log-likelihood function,
taking into account that the numerical procedures needs to be updated for
each iteration in the maximization procedure?
Any help will be much appreciated.
Kristian
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