Imperial/Dry Lab/Data Analysis
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==Principle of method of parameter extraction== | ==Principle of method of parameter extraction== | ||
| - | The method used weighted non-linear leasts-squares. This technique involves obtaining the best-fitting non-linear curve | + | The method used weighted non-linear leasts-squares. This technique involves obtaining the best-fitting non-linear curve for a given set of parameters from the parameter space. This procedure involves minimizing the sum of the squares of the offsets from the chosen curve. [http://mathworld.wolfram.com/LeastSquaresFitting.html] Here, the offsets refering to the difference between the chosen non-linear curve and the experimental data, at a particular value of the independent variable. |
A weighted non-linear least-squares is used, so that that the integrity of the data does not corrupt the extracted parameters. Weightings are assigned to adjacent experimental data points, according to their variance from the general trend/behaviour. | A weighted non-linear least-squares is used, so that that the integrity of the data does not corrupt the extracted parameters. Weightings are assigned to adjacent experimental data points, according to their variance from the general trend/behaviour. | ||
====Representative example==== | ====Representative example==== | ||
Consider the following model | Consider the following model | ||
Revision as of 15:02, 22 October 2007
Contents |
Data Analysis
Introduction
Data analysis involves manipulating experimental data with the objective of extracting useful information. This then allows us to test our original hypotheses surrounding the problem, and in doing so, test the stringency/validity of our representative model.
If the model proves to be valid, data analysis likewise provides a means of parameter extraction essential in rendering our theoretical model more realistic (as it gleans parameters from actual expimental data).
Our approach to data analysis utilizes curve/shape-fitting by non-linear regression (employing the least-squares method).
Principle of method of parameter extraction
The method used weighted non-linear leasts-squares. This technique involves obtaining the best-fitting non-linear curve for a given set of parameters from the parameter space. This procedure involves minimizing the sum of the squares of the offsets from the chosen curve. [http://mathworld.wolfram.com/LeastSquaresFitting.html] Here, the offsets refering to the difference between the chosen non-linear curve and the experimental data, at a particular value of the independent variable. A weighted non-linear least-squares is used, so that that the integrity of the data does not corrupt the extracted parameters. Weightings are assigned to adjacent experimental data points, according to their variance from the general trend/behaviour.
Representative example
Consider the following model
