Latin for "from after the fact."
A method of concluding there is a significant statistical relationship by the interpretation of statistical data obtained without a control group.
Generally considered not sufficiently convincing (even fallacy - jumping to conclusion), though sometimes it is the only method available, as in medicine, at least in the cases where research with a control group might involve inflicting a disease on the test group.
For example, statistical data shows a higher occurence of certain diseases among smokers. Stating that smoking is the cause of those diseases is an ex post facto conclusion.
Strictly speaking, it is theoretically possible there is some other cause, one that makes a person more likely to become a smoker and to be afflicted by diseases that occur more often among smokers (i.e., even if he managed not to become a smoker, he would still get the disease because of the underlying cause).
The only way to prove that smoking is the cause of those diseases would be by randomly selecting two groups of youngsters, and make one smoke, the other not smoke for the rest of their lives, then test both groups for the development of those diseases. This, naturally, is not a realistic proposition (for ethical reasons to say the least).
Note: I am not disputing whether smoking causes certain diseases, I am just using it as an example of where ex post facto interpretation of statistical data may be the only viable option, though otherwise considered an incorrect way of data interpretation.