How to know which set is most likely to have been generated by some probability distribution? I have 3 sets of points in $R^n$: $X$, $A$ and $B$, how can I (preferably quickly) check which of the two sets $A$ and $B$ is most likely to have been generated by the same probability distribution as $X$ was generated by?

Perform a two-sample Kolmogorov-Smirnov test between $X$ and $A$. Perform another two-sample KS test between $X$ and $B$. If the first test has the highest p-value, choose $A$. Otherwise choose $B$ as the most likely distribution.
Update: Given that you have vectors, you could do $n$ one-dimensional KS tests and see if there is a preponderance of p-values favoring $A$ or $B$. Another option: Look at Kullback-Leibler divergence.
