Troubleshooting NonlinearModelFit in Mathematica

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SUMMARY

The discussion centers on troubleshooting the NonlinearModelFit function in Mathematica while attempting to model the formation and decay of pyrene excimer fluorescence. The user is struggling to obtain convergence for all four coefficients (A, B, ka, kb) in the equation I(t) = -Ae-kat + Be-kbt. It is established that non-linear function fits are sensitive to initial parameter values, and adjusting these starting guesses may resolve the convergence issue. The user is encouraged to consult the Mathematica help menu for guidance on using NonlinearModelFit effectively.

PREREQUISITES
  • Familiarity with Mathematica software
  • Understanding of non-linear regression analysis
  • Knowledge of fluorescence kinetics and modeling
  • Ability to manipulate and analyze data files in Mathematica
NEXT STEPS
  • Explore the NonlinearModelFit function in Mathematica documentation
  • Learn how to set initial parameter values in NonlinearModelFit
  • Investigate methods for estimating standard errors and confidence levels in Mathematica
  • Review techniques for plotting data and fit functions in Mathematica
USEFUL FOR

Students and researchers in chemistry or physics, particularly those working with fluorescence kinetics and using Mathematica for data analysis and modeling.

cep
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Hello, I'm working on this Mathematica assignment, just basic tutorial-type stuff (you can ignore the details about pyrene, not important), and the fit on this function won't converge. Someone in my class said it converged fine, so I was wondering if anyone notices any errors in my work. Alternatively, can you think of any alternative ways to express the function?

Thanks!

Homework Statement




3. Formation and Decay of Pyrene Excimer in Solution

The traces for pyrene fluorescence (see Experiment 3) show a fast rise and a slower fall processes which correspond to a complex kinetic of the formation and decay of the pyrene excimer in solution. The evolution of the excimer fluorescence intensity I(t) in time t can be described by the following equation:

I(t) = -Ae-kat+Be-kbt

Data are provided in a file “emission_data” with time given in the first column, while the fluorescence intensity given in the second column.

REPORT:
(1) Find coefficients A, B, ka and kb. Estimate standard error and confidence levels for these parameters. Hint: see Mathematica help menu for function NonlinearModelFit.
(2) Provide plot of data with the superimposed fit function


Homework Equations



Mathematica knowledge

The Attempt at a Solution



See attached screenshot.

I can get 3/4 coefficients, but I don't know if they're correct due to the fourth one failing to converge, and I can't make the plot without all coefficients!
 

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Non-linear function fits can be very sensitive to the starting values of the function parameters. I'd think there would be an option to provide starting 'guesses'. If so, playing around with the starting values could fix the problem.
 

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