For the mathematical optimisation of the single model-free models, the local tm model-free models, the diffusion tensor, or the global model of the diffusion tensor together with all model-free models, it is the chi-squared value which is minimised. For these situations the number of parameters remains constant. Hence the result of optimising the chi-squared value or the AIC value is identical.
Essentially, the chi-squared value is used to compare two instances of the same model (with different parameter values) while the AIC value is used to compare two different models! The iterative procedure used in the new model-free optimisation protocol, which is implemented in 'full_analysis.py', is a very different concept! That is because at each iteration the global model is different (well until convergence that is). Hence in this situation, chi-squared values between iterations cannot be compared as the models are different. But AIC can be used to compare these different models. As I discussed in my JBNMR, 2003 publication on model-free model selection, AIC is an attempt to approximate what is known as the Kullback-Leibler discrepancy. This discrepancy is a powerful concept - it is a measure of how close the model fits the data independent of the noise associated with that data. This is an embodiment of parsimony - the model with the lowest discrepancy value is that which is closest to Occam's razor. Therefore what this new protocol does is optimise the chi-squared value within one iteration and then optimise the Kullback-Leibler discrepancy between iterations. I have used set theory to mathematically express these concepts and mathematically encapsulate the entire problem, but that explanation will have to wait until my papers are published! The answer to your question is simply that there is no difference between the two in finding the correct model-free parameters for a single model. However because the model-free parameter values are intricately linked to the diffusion tensor parameters and vice versa, you have a chicken-and-egg scenario in which the new protocol optimises the AIC value between iterations. Have I now completely confused you? Edward On 10/6/06, Alexandar Hansen <[EMAIL PROTECTED]> wrote:
I have a question about the AIC statistic. Let's say we're optimizing model 2 (S2 and te). As it searches for a minimum, wouldn't the difference between chi2 and AIC just be AIC = chi2 + 4? If so, I guess I don't understand the difference between the two in finding the correct model free parameters. Alex _______________________________________________ relax (http://nmr-relax.com) This is the relax-users mailing list [email protected] To unsubscribe from this list, get a password reminder, or change your subscription options, visit the list information page at https://mail.gna.org/listinfo/relax-users
_______________________________________________ relax (http://nmr-relax.com) This is the relax-users mailing list [email protected] To unsubscribe from this list, get a password reminder, or change your subscription options, visit the list information page at https://mail.gna.org/listinfo/relax-users
