Team:Paris/Network analysis and design/Core system/Model construction/Akaike
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= Experiment = | = Experiment = | ||
* As an experiment, we wished to compare the two models presented below : | * As an experiment, we wished to compare the two models presented below : | ||
- | '''System#1''' : using the linear equations | + | '''System#1''' : using the linear equations found in bibliography :<br> |
[[Image:syste_akaike_1.jpg|center]]<br> | [[Image:syste_akaike_1.jpg|center]]<br> | ||
'''System#2''' : using classical Hill functions :<br> | '''System#2''' : using classical Hill functions :<br> | ||
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[[Image:plotAkaikeBob.jpg|400px|left|thumb|Bob Model]] | [[Image:plotAkaikeBob.jpg|400px|left|thumb|Bob Model]] | ||
[[Image:plotAkaikeHill.jpg|400px|right|thumb|Hill Model]] | [[Image:plotAkaikeHill.jpg|400px|right|thumb|Hill Model]] | ||
- | <br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br>Then, we see that the | + | <br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br>Then, we see that the model that uses linear equations does not fit that well, but under certain conditions it is not so bad. Indeed, if the data set is short, this kind model is a reluctant model since it is eases the understanding of the dynamics. |
* Consequently, what have we proved? These results show that: | * Consequently, what have we proved? These results show that: | ||
** Firstly, we may see that the AICc does converge to AIC for greater values of n. | ** Firstly, we may see that the AICc does converge to AIC for greater values of n. | ||
** Then, we may see that, as predicted, System#2 is not penalized anymore for greater values of n, although System#1 is. Consequently, we may adapt our system knowing the length of the data set we are going to obtain experimentally. | ** Then, we may see that, as predicted, System#2 is not penalized anymore for greater values of n, although System#1 is. Consequently, we may adapt our system knowing the length of the data set we are going to obtain experimentally. | ||
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** However, since for a larger set of data System#2 minimizes the criteria, these criteria cannot decide whether a model is "better" than another one, since those criteria are arbitrary. Yet, they may help us find a better compromise between simplification and accuracy. | ** However, since for a larger set of data System#2 minimizes the criteria, these criteria cannot decide whether a model is "better" than another one, since those criteria are arbitrary. Yet, they may help us find a better compromise between simplification and accuracy. | ||
** One must be careful when building a model, since chosing the number of parameters and deciding how deep one wishes to go into detail, influences the goal and the results of a model. It is therefore important to understand that a model has to be conceived to achieve a precise aim. | ** One must be careful when building a model, since chosing the number of parameters and deciding how deep one wishes to go into detail, influences the goal and the results of a model. It is therefore important to understand that a model has to be conceived to achieve a precise aim. | ||
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= A fundamental tool? = | = A fundamental tool? = |
Revision as of 16:31, 25 October 2008
Depending on the experimental constraints, how can we be helped by mathematical criterions ?
Short introduction to the criteria
where n denotes the number of experimental values, k the number of parameters and RSS the residual sum of squares. The best fitting model is the one for which those criteria are minimized.
Experiment
System#1 : using the linear equations found in bibliography : System#2 : using classical Hill functions :
A fundamental tool?Why can we introduce this seemingly awkard criteria as being a fundamental tool? This precise criteria enables the mathematician to adapt its model. In fact, in that respect, conducting this analysis over his model gives tangible arguments to the mathematician to use such and such model. Indeed, for example in our precise case, if we have about 20 experimental points to fit, BOB approach is sufficient. However, if we get 50 points, BOB approach would be inadequate compared to APE. We believe that this kind of criteria is an essential tool, that might help the model maker to comprehend and control the assumptions he made while creating his model.
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