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. | ||
- | * Akaike and Schwarz criteria met our demands : | + | * Akaike and Schwarz criteria taken from the information theory met our demands quite well : |
Akaike criterion : [[Image:AIC.jpg|center]] | Akaike criterion : [[Image:AIC.jpg|center]] | ||
Hurvich and Tsai criterion : [[Image:AICc.jpg|center]] | Hurvich and Tsai criterion : [[Image:AICc.jpg|center]] | ||
Schwarz criterion : [[Image:BIC.jpg|center]] | Schwarz criterion : [[Image:BIC.jpg|center]] | ||
where n denotes the number of experimental values, k the number of parameters and RSS the residual sum of squares. | 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 | + | The best fitting model is the one for which those criteria are minimized. |
- | * As an experiment, we wished to compare two models presented below : | + | * It is remarquable that Akaike criterion and Hurvich and Tsai criterion are alike. AICc is therefore used for small 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. In addition, Schwarz criterion is meant to be more penalizing. |
- | System #1 : using the linear equations : [[Image:syste_akaike_1.jpg]] | + | * As an experiment, we wished to compare the two models presented below : |
- | System #2 : using classical Hill functions : [[Image:syste_akaike_2.jpg]] | + | System#1 : using the linear equations from our BOB approach : [[Image:syste_akaike_1.jpg]]<br> |
- | + | System#2 : using classical Hill functions : [[Image:syste_akaike_2.jpg]]<br> | |
+ | * We made a set of data out of a noised Hill function. In fact, our data set was made by using the same equations as System#2, but we introduced a normal noise for each point. Thus, System#1 is penalized because its RSS will be greater than that of System#2. Nevertheless, System#2 will be more penalized by its number of parameters. | ||
Revision as of 12:40, 3 September 2008