Team:Paris/Modeling/BOB/Akaike

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* Using linear equations in a biological system might seem awkards. However, we wanted to check the relevance of this approach. We have been looking for a criterium that would penalize a system that had many parameters, but that would also penalize a system which quadratic error would be too important while fitting experimental values.
* Using linear equations in a biological system might seem awkards. However, we wanted to check the relevance of this approach. We have been looking for a criterium that would penalize a system that had many parameters, but that would also penalize a system which quadratic error would be too important while fitting experimental values.
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* The answer was given by the Akaike and Schwarz criteria :
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* Akaike and Schwarz criteria met our demands :
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[[Image:AIC.jpg|center]]
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Akaike criterion : [[Image:AIC.jpg|center]]
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[[Image:AICc.jpg|center]]
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Hurvich and Tsai criterion : [[Image:AICc.jpg|center]]
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[[Image:BIC.jpg|center]]
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Schwarz criterion : [[Image:BIC.jpg|center]]
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where n denotes the number of experimental values, k the number of parameters and RSS the residual sum of squares.
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* It is remarquable that Akaike criterion and Hurvich and Tsai criterion are alike. AICc is therefore used for smal sample size, but converges to AIC as n gets large. Since we will work with 20 points for each experiment, it seemed relevant to present both models.
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* As an experiment, we wished to compare two models presented below :
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[[Image:syste_akaike_1.jpg]][[Image:syste_akaike_2.jpg]]
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METTRE LES CRITERS
 
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EXPLIQUER THEORIE INFO RAPID
 
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EXPLIQUER DIFFERENCE ENTRE CRITERES
 
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EXPLIQUER PROTOCOL SIMULATION
 
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DONNER RESULTS
 
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Mettre prgrms eventually
 

Revision as of 12:27, 3 September 2008

(Under Construction)

Model Comparison
  • Using linear equations in a biological system might seem awkards. However, we wanted to check the relevance of this approach. We have been looking for a criterium that would penalize a system that had many parameters, but that would also penalize a system which quadratic error would be too important while fitting experimental values.
  • Akaike and Schwarz criteria met our demands :
Akaike criterion :
AIC.jpg
Hurvich and Tsai criterion :
AICc.jpg
Schwarz criterion :
BIC.jpg

where n denotes the number of experimental values, k the number of parameters and RSS the residual sum of squares.

  • It is remarquable that Akaike criterion and Hurvich and Tsai criterion are alike. AICc is therefore used for smal sample size, but converges to AIC as n gets large. Since we will work with 20 points for each experiment, it seemed relevant to present both models.
  • As an experiment, we wished to compare two models presented below :

Syste akaike 1.jpgSyste akaike 2.jpg




We mostly used the definition of the criteria given in : [http://www.liebertonline.com/doi/pdf/10.1089/rej.2006.9.324 K. Kikkawa.Statistical issue of regression analysis on development of an age predictive equation. Rejuvenation research, Volume 9, n°2, 2006.]

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