Interpreting predictions of RFs based on AUCs If I have a random forest of old independent data with an AUC of .66, a random forest of new independent data with an AUC of .75, and a random forest of old and new independent data with an AUC of .79, what can I inference by the AUC of the old+new independent data, given the AUCs previously mention.
EDIT: These are all validation AUCs. All RFs were trained on and for a binary classification outcome using 4 explanatory continuous variables for the new data, one explanatory continuous variable for the old data.
 A: Having more data usually makes models better. I don't think that there's much more to be said.
A: 
using 4 explanatory continuous variables for the new data, one
  explanatory continuous variable for the old data

So for the new model you used something like y ~ x1 + x2 + x3 + x4, but in the old model it was just y ~ x1?
If this is correct then it's not a surprise that you registered a higher AUC.
Also is x1 in the new model the same as x1 in the old model? I mean the same variable. Because if that's the case you could say that x1 impacts heavily on performance, but x2-x4 improve accuracy too.
You should compare the performance that you have between the old and new model (plus the old+new model), using the same explanatory variables (same number, same variables).
Also the number of observations should be the same for a meaningful comparison between the models.
If observations are randomly picked than you should also repeat k times for consistency, ie: repeat the 3 models on n observation sampled from your population.

what can I inference by the AUC of the old+new independent data, given
  the AUCs previously mention

To me not much, because as I mentioned above the models are different. Try use the same number of variables first.
