Comment author:ciphergoth
17 March 2010 02:44:00PM
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Can you be clearer? Log likelihood ratios do add up, so long as the independence criterion is satisfied (ie so long as P(E_2|H_x) = P(E_2|E_1,H_x) for each H_x).

Comment author:Academian
17 March 2010 02:56:52PM
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Sure, just edited in the clarification: "you have to multiply odds by likelihood ratios, not odds by odds, and likewise you don't add log odds and log odds, but log odds and log likelihood-ratios".

It explains "mutual information", i.e. "informational evidence", which can be added up over as many independent events as you like. Hopefully this will have restorative effects for your intuition!

## Comments (211)

Best*0 points [-]Can you be clearer? Log likelihood ratios do add up, so long as the independence criterion is satisfied (ie so long as P(E_2|H_x) = P(E_2|E_1,H_x) for each H_x).

Sure, just edited in the clarification: "you have to multiply odds by likelihood ratios, not odds by odds, and likewise you don't add log odds and log odds, but log odds and log likelihood-ratios".

As long as there are only two H_x, mind you. They no longer add up when you have three hypotheses or more.

Indeed - though I find it very hard to hang on to my intuitive grasp of this!

Here is the post on information theory I said I would write:

http://lesswrong.com/lw/1y9/information_theory_and_the_symmetry_of_updating/

It explains "mutual information", i.e. "informational evidence", which can be added up over as many independent events as you like. Hopefully this will have restorative effects for your intuition!

Don't worry, I have an information theory post coming up that will fix all of this :)