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I: NONLINEARMODELFIT

• To: mathgroup at smc.vnet.net
• Subject: [mg120297] I: NONLINEARMODELFIT
• From: maria giovanna dainotti <mariagiovannadainotti at yahoo.it>
• Date: Sun, 17 Jul 2011 06:03:44 -0400 (EDT)

Dear Mathematica Group,

I am fitting a function of 3 parameters with the NonlinearModelFit
and with the Marquardt Levemberg algorithm.  Since  this method gives
the interval of the Parameters of the best fit considering the parameters
not correlated, I was looking for a tool that takes into account the
fact that the parameters are correlated and the  parameters interval
should respect the following rule:

The confidence interval for a given parameter should be computed by
varying the parameter value until the chi^2 increases by a particular
amount above the minimum, or best-fit value.  The amount that the chi
square is allowed to increase (also referred to as the critical
delta_chi^2) depends on the confidence level one requires, and on
the number of parameters whose confidence space is being calculated.
The critical delta_chi^2 for common cases are given in Avni, 1976:
 For example in the case I am using for 3 parameters delta_chi^2=3.50.

I would be very grateful if someone of you is acquainted with a such
a tool in Mathematica or some of you has done a code to sort this
problem out.  Thanks a lot in advance for your help.

Best regards,

Maria