What is the best mathematical tool to fit observational data with theory?
Hi Razieh, whats happens is that as you know, there is not match with the observational and the theoretical, that is the missing mass problem.. so what most physicists do is the consider DM, and the error bars match on the observational curve. By another hand, i think that there is problem with that about DM, because what you have to fit is far away of the disk dynamic, means in that region you must to maintain the usual Kleplerian behaviour, so.. i think that is not a problem os some exoctic mass but of the gravitation theory that rules the out side disk region
HI
The simples answer from the point of view of theoretical physisits is -- the mathematical beauty and simplicity of the well established symmetry and geometrical principles of your theoretical model
Exactly! Dear Adriana as you know, observation of galaxies reveal that there is a discrepancy between the observed dynamics and the mass inferred from the luminous matter, so an alternative approach to the problem of missing mass ,is to replace DM with a modified gravity theory (MOG) and we do not forget that it must be a generally covariant one!
Looking at earlier discussion I have an impression that you are asking about hypothesis testing rather than data fitting. Those problems are related but otherwise different. But perhaps my impression is incorrect, so I switch to the original question. Probably the most popular is LSQ (Least Squares) method. It will always produce some results, even when you fit a straight line to observations scattered over (semi)circle. We like it anyway, as the roots of this method are connected with the name of Carl Friedrich Gauss. Newer approach is Maximum Entropy Method presented more than 50 years ago by Jaynes. Today some researchers prefer to use either the 'mindless' Monte Carlo guessing or 'intelligent' searches like genetic algorithms, neural networks or artificial ant's colony, and a plethora of similar, 'nature inspired' methods (--> papers by Xin She Yang).
My own favorite is not yet published method, extensively using --> interval arithmetic (see Wikipedia, if you don't know what it is). It is able to fit searched parameters to the observed data, together with reliable estimates of their uncertainties, not only to ordinary formulas but to implicit expressions as well. Contact me individually, if you want to see almost finished draft of my method.
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