Hi I was looking for some tutorials about the maximum likelihood approach for the modelling of multi response data for kinetics for implementation in Matlab/Mathematica or other programming languages, I was trying to look for some tutorials or scripts which could help to understand the theory.. Could you help me please? Further, I was looking also for some free software about the same method..
Hello,
here are some links which are using R language for maximum likelihood.
http://www.stat.umn.edu/geyer/5931/mle/mle.pdf
https://stat.ethz.ch/R-manual/R-devel/library/stats4/html/mle.html
Gianfranco.
In the attached link you will find an example on parameter estimation with a system described by ODE's. It uses lmfit optimization interface in Python (a nice wrapper around scipy optimizers) and odeint to integrate the ODE sytem. Python is a good choice since you are looking for a free tool to deal with the problem, and its syntaxis is not very different from Matlab's, so if you have any experience on the latter, you'll be fine.
Lmfit also has a nice way to sample posterior probability distributions (bayesian analyses, as far as I know) through its emcee method. You can then plot the correlations between factors and see the used distributions with corner package (separate installation). I also let lmfit webpage for you to explore it.
Finally, I recommend you to read these book chapters, to get insights on the kind of problem you are dealing with:
1. Chapter VIII in "Nonlinear Parameter Estimation" by Bard.
2. Chapter 9 in "Nonlinear Programming" by Biegler.
Hope it helps!
Best,
https://people.duke.edu/~ccc14/sta-663/CalibratingODEs.html
https://lmfit.github.io/lmfit-py/index.html
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