Least squares procedure for fitting (theoretical) models to (experimental) data

[dciurchea]

I. Systematic errors (mistakes) should be removed. It is better to change the measuring method. No analysis is valid in presence of sytematic errors. 

II. In absence of systematic errors the postulates below define the normal distribution (Gauss' bell)- for a single x sampled many times


 1. Measurement results are affected by random errors only;

 2. Deviation of result x from the true value is caused by n random factors, each producing an elementary error;

 3. Cases yielding random errors are independent one from another;

 4. Likelihood(probability) of positive errors is equal to the likelihood of negative errors.

 5. Very large errors have the same probability of occurrence with very small errors.


III. In modelling experimental data where measurements are a function of x (many x) and every measurement is expected to be free of systematic errors, that is described by the normal distribution at II.  The least squares functional may be used to adjust model parameters:

sum for every x of (y_measured(x) -y_calculated(y)) squared = minimum

In order to get the right values for the parameters, the minimum is searched. Note that the order in performing sumation is arbitrary.

IV. according to the analytical form of the "y_calculated" function, a computer code should be written in order to allow getting the right parameter of the model according to the analytical model assumed. That is, the model anlytical shape is assumed by the author. 

Interestingly, by writing the program allowing for minimization, the author solves the problem while while the actual numeric values may be relevant or not.

Therefore, by indicating a MODEL (of reading Jordanes) which minimizes the the error in FITTING independent events and data, otherwise mysterious, we have applied a least squares procedure. 

The "parameters" adjusted especially indicate an uniform religious pattern in pre-christian era in "barbarian" Europe, well conserved in the Eddas-with an important role of ressurection, thought to be effective. 

Proper understanding of local toponimics, geography and folklore elements of antic Dacia was helpful.

Refs:http://download.academic.ro/ebook/index.htm

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