- On 3 Mar 1997 at 12:19:55, "J. Zhu" (jyzhu.aaa.usa.net) sent the message

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Hi there, a couple of graduate students bring up the following

questions. How are you sure that your nonlinear curve-fitting in the

modeling process converges to global minima not local minima. One of

methods to check if the results reach global minima seems to change

initial estimates to 10 or more times of the original values. It assumes

global minima achieve if the same results are obtained from different

initial estimates. The questions are what to do in the cases (1) the

initial estimates of first time reach global minima while the initial

estimates of second time reach local minima; and (2) the initial

estimates of first time reach local minima while the initial estimates

of second time reach another local minima. Also, how to select the

initial estimates of second time in a case where many parameters, say

25, need to be estimated, all or parts (how many) in a time change? What

about some parameter estimates in global minima and some in local

minima. Another question no related to the minimal issue is what=92s

minimal ratio of data (sample) points to the numbers of parameters to be

estimated for ideal curve-fitting. Thank you very much for your opinions

and comments.

Johnny

Emailto:jyzhu.at.usa.net - On 4 Mar 1997 at 13:05:55, "Vladimir Piotrovskij" (VPIOTROV.-at-.JANBELC1.SSW.JNJ.COM) sent the message

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First, be sure your model is not over-parameterized. Check the

parameter correlation matrix, and if you find a lot of 0.9 or higher

values in it, your model should be reduced. If you have the right

number of well-defined parameters in the model, you will hardly have

got any problems with local minima. Many curve fitting programs

produce the correlation matrix.

Then, each time you fit a model to your data, examine the plot of

residuals against the independent variable. If residuals are randomly

scattered around zero, most probably you've got a global minimum.

There are no common rules concerning the number of points needed per

parameter. This issue is only a part of the problem of study design.

The number of points depends not only on the complexity of your model

(linear or nonlinear, etc.) and on its sensitivity with respect to

changes in parameters, but also on the magnitude and the structure of

the random noise in your data.

Vladimir

vpiotrov&janbe.jnj.com - On 5 Mar 1997 at 11:38:18, Jean Debord (jdebord.-at-.MicroNet.fr) sent the message

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There are methods known as global optimization which (in principle)

localize the

global minimum. Simulated annealing (SA) is one of them. It allows the

objective

function to "escape" from a local minimum with a probability computed

according to

Boltzman's law. There are several SA codes available on the Internet (see

for instance

Lester Ingber's web page at http://www.ingber.com/).

I am not aware of any application of these techniques in Pharmacokinetics,

however.

The only biological references that I have found dealt with the

minimization of

protein structures.

Sincerely,

--

Jean Debord

Laboratoire de Pharmacologie, Faculte de Medecine

2 Rue du Docteur Marcland, F-87025 Limoges, France

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