Why Likelihood?
Malcolm Forster, Elliott R. Sober · 2004
The likelihood principle has been defended on Bayesian grounds, with proponents insisting that it coincides with and systematizes intuitive judgments about example problems, and that it generalizes what is true when hypotheses have deductive consequences about observations. Richard Royall offers three kinds of justification. He points out, first, that the likelihood principle makes intuitive sense when probabilities are all 1s and 0s. His second argument is that the likelihood ratio is precisely the factor that transforms a ratio of prior probabilities into a ratio of posteriors. His third line of defense of the likelihood principle is to show that it coincides with intuitive judgments about evidence when the principle is applied to specific cases. This chapter divides the principle into two parts—one qualitative, the other quantitative—and evaluates each in the light of the Akaike information criterion (AIC). Both turn out to be correct in a special case (when the competing hypotheses have the same number of adjustable parameters), but not otherwise.