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Re: High-dimensional Minimization without analytical derivatives



Maximizing a likelihood function with 17 parameters and
80 observations is likely to get you odd answers, e.g., many
of your estimates will be on the boundary of the parameter space.

Another possible approach is a Bayesian one: define some reasonable
prior distributions for your parameters, then run a simulation to find
the regions where your posterior density function is highest. A common
simulation algorithm here is the Metropolis-Hastings algorithm, about
which there is a lot of literature. One popular book is "Markov Chain
Monte Carlo in Practice" by W. R. Gilks, S. Richardson,
D. J. Spiegelhalter. Coding such a simulation isn't difficult.

With MCMC simulations, you can also specify the dimension of the
parameter vector as a parameter itself. Peter Green wrote a paper
about this:

Reversible jump Markov chain Monte Carlo computation and Bayesian
model determination, Biometrika, 82, 711-732 (1995)

-Jason

On Mon, Aug 30, 2004 at 05:11:11PM -0500, Anatoliy Belaygorod wrote:
> Hello,
> I need to find a (local) maximum of my likelihood function with 80 datapoints over the 17-dimensional parameter space. I want to use gsl_multimin_fdfminimizer_vector_bfgs, (or some other gradient-based algorithm), but I would really hate to specify 17 (or maybe much more if we change the model) analytic derivatives. 
> Can you please tell me if I have better options? Can I use the one-dimensional numerical derivatives gsl_diff_central instead of analytic ones when I write "my_df" function for BFGS? How would this approach (if it is feasible at all) compare to Nelder Mead Simplex algorithm provided in my version of GSL 1.4? Is there a better option that would involve numerical gradient evaluation coupled with BFGS method?
>  
> I really appreciate any help or advice you can give me.
> Sincerely,
> Anatoliy
>  
> 

-- 
jstover@sdf.lonestar.org
SDF Public Access UNIX System - http://sdf.lonestar.org


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