Modelling a probability distribution on different feature sets I have a binary classification problem, and I use method A and method B to extract features, F1 and F2, for this problem from dataset X. Now, I train two models, y1 and y2, separately on the two extracted feature sets. Concretely:
p(y1 | F1) = ...
p(y2 | F2) = ...

Now I chain them together:
Y = p(y1 | F1) * p(y2 | F2)

And if the result of the above multiplication is greater than 0.5, I decide that the test example belongs to classification set 1.
Is this approach correct? 
 A: Yes and no - your method might work for the problem you have at hand, but it is certainly not the most principled way to combine the two methods.  There is a huge literature on the best way to combine classifiers, either by using distinct learning algorithms trained on the same data (ensemble learning), or using different datasets or feature extraction methods (as in your case).
The key question you need to answer is the following: what is the relative "status" of your two methods A and B?  Is one more reliable or trustworthy than the other? Would you rather use the two methods in parallel, or use the second method as a "back-off" mechanism in case the first method does not produce classification with high enough confidence?  There are plenty of ways to combine classifiers.
In any case, simply multiplying the probabilities of the two classifiers will likely produce strange results, and will not produce a proper probability distribution if you don't renormalise.  I you want to use the results of both classifiers, I would rather go for a (weighted) sum of probabilities from the two classifiers.
