I have performed some metabolomic analysis of different tumor sites and would like to see if there are any correlations between the metabolite leves and some of the tumor characteristics that I am interested in.

These correlations (if they exist) do not necessary have to be linear relations, so I was trying to undestand how to select the best model that would fit my data and to determine if the fit is accurate.

As far as I understand, you can calculate the Akaike Information Criterion (AIC) for each of the individual fits and, in theory, the lower the AICof a model, the better the model fits the actual data points.

My questions are:

1) Am I correct in my understanding of how AIC works?

2) Should I be using other parameters in addition/instead of AIC

3) Lets say I have a dataset that has no true correlation whatsoever. If I attempt to perform non-linear fitting of this data, I will still obtain a value for AIC, that I can compare between models to determine what fits best. However, since there is not really any correlation, this model will be largely worthless. Is there an absolute value of AIC, at which one can simply say, "this model does not fit the data at all?"

4) As a follow-up to the previous question, if there is a paramater whose value can be used to determine if a model fits the data well, can that parameter/set of parameters be used to calculate a probability of fit, akin to having a p-value calculated for linear correlation? (from what I read, this is much more difficult for non-linear correlations, but I wanted to make sure.

Thank you for your help in advance. Let me know if something is unclear.