Marc Mazerolle, whom I criticized on p. 216 of the book for saying that Akaike weights were probabilities (rather than being "similar to" probabilities or other such waffle-words), sent me a nice e-mail to point out that (1) the relevant chapter of his thesis is published in *Amphibia-Reptilia* [1] and (2) David Anderson's book, *Model-based inference in the life sciences* [2] explicitly says (on p. 88) that "A given $w_i$ is the probability that model $i$ is the expected K-L best model". (*Please excuse the bibliographic glitch, if you're looking at this on the main blog page: it's a technical issue I don't know how fix.*)

(continue)

Well, Mazerolle is right (that Anderson says weights are probabilities): I don't have the book (although I should probably buy it), but I was able to look the page up in Google books. Scary as it is for me to criticize such a smart guy/big shot, I think Anderson is being sloppy here (which is unusual): he starts out by saying

These weights are also Bayesian posterior model probabilities (under the assumption of savvy model priors) …

(which is correct) but then slides into the sentence quoted above,

A given $w_i$ is the probability that model $i$ is the expected K-L best model

As far as I know, this statement is only true with that particular choice of "savvy" priors (which IMO are fairly odd — you can read about them in Burnham and Anderson's work), and is only true asymptotically (i.e. when the data set is very large: I'm not sure about this, but I think so, by analogy with other criteria like the BIC).

In thinking about the bottom line, I thought of the phrase "you can't have your cake and eat it too" — which as it turns out is *exactly* what I said in the original footnote referring to this mistake:

Taking AIC weights as actual probabilities is trying to have one’s cake and eat it too; the only rigorous way to compute such probabilities of models is to use Bayesian inference, with its associated complexities (Link and Barker, 2006).

So there!