Dear R-users,
My task is to fit two-dimensional density functions to grid data obtained by
counting particles within grid cells. By use of the adapt method I get a nume
rical integral of the density function for each grid cell. By use of the nlm
method I can minimize the Log Likelihood function. By nlm iteratively calling
adapt it should be possible to estimate the density function parameters.
However, the adapt function may change the number of points used for integrat
ion per grid cell as the parameters of the density functions change. This may
cause (very small) changes in the precision of integration which causes (sma
ll) jumps in the Likelihood function. This may be a problem when gradients of
the Likelihood function are small close to the minimum. I have inspected the
number of points per grid cell used for function evaluation by adapt (minpts
). When these do not change from one iteration to the next it is likely that
the same points were used. However, a more satisfactory solution might be to
fix the points used by adapt for shorter runs (e.g. five iterations). Is this
possible?
Alternatively, is it possible to output the points used by adapt for repeated
use in another integration procedure? This might reduce computation time.
Minimization:
In some cases I have to estimate 6-8 parameters (when population sizes are in
cluded), and the likelihood function may have several local minima.
Will the (combined) use of one or more algorithms in the optim method be more
efficient than the nlm method?
Perhaps this is a nasty task. Any suggestions for solutions are well come! If
suitable methods exist in Java the omega-hat R - Java interface would allow
the use of these.
Can any non-specialist references on these subjects be recommended?
Thanks in advance,
Karsten
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