TITLE: Applications of cohomology to probability and statistics
QUESTION [10 upvotes]: Are there interesting/useful applications of cohomology (and homological algebra in general) to probability and statistics, or information theory?
By "interesting/useful", I mean "not merely descriptive", that is, they can actually say something new and not just formalize well known concepts. 
For example, I have recently found this paper, which addresses dually flat manifolds (and so, indirectly, information geometry). 
Any other examples I have missed?
Thanks!
(Feel free to edit tags appropriately.)

REPLY [10 votes]: There is a very nice interpretation of entropy as a cohomology class by Baudot and Bennequin which you can read about HERE.
In general, I strongly believe that there is an underlying topological content to parts of information theory- as there is information geometry, there will be information topology.