[R] Combined use of the nlm and adapt methods

[Chong Gu]

You may want to check out smolyak.quad in the gss package.


> 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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