My money’s on -22 days.

]]>Jonathan:

Yup, the likelihood ratio is what it is (conditional on the model being correct). What to do about it is another story.

]]>He covers that objection. Yes, you need two hypotheses to create a likelihood ratio, but there is no reason that you have to pick those hypotheses before you see the data. Now, whether someone is going to be *convinced* by forking paths hypotheses you only created after you saw the data is obviously very problematic — no one is. But Royall argues (to me) persuasively that likelihood ratios are just calculations.

]]>Nothing has jumped. Only if he had mentioned a deck consisting only of the 7 of hearts before pulling out this specific card…

]]>This reminds me of Richard Royall’s book on likelihood inference which was very influential on me. He gives the example of taking a deck of cards, pulling out a card, getting, say, the 7 of hearts, and then pointing out that on a pure likelihood basis, the odds of a normal deck versus a deck consisting only of the 7 of hearts is 1:52. The likelihood of a deck consisting entirely of 7s of hearts has jumped 52-fold. He then discusses the importance of the prior, which ought to be different if you bought the deck in a store versus from a magician, for example.

]]>This, and it nicely illustrates the meaning of “prior information”.

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