Team:Paris/Modeling/BOB/Akaike

(Under Construction)

• 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 :

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 :

System #1 : using the linear equations : System #2 : using classical Hill functions :

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.]