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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