Two Bayesian approaches to choosing between statistical models are contrasted. One of these is an approach which Bayesian statisticians regularly use for motivating the use of AIC, BIC, and other similar model selection criteria, and the other one is a new approach which has recently been proposed by Bandyopadhayay, Boik, and Basu. The latter approach is criticized, and the basic ideas of the former approach are presented in a way that makes them accessible to a philosophical audience. It is also (...) pointed out that the former approach establishes a new, philosophically interesting connection between the notions of simplicity and informativeness. (shrink)

Recent solutions to the curve-fitting problem, described in Forster and Sober ([1995]), trade off the simplicity and fit of hypotheses by defining simplicity as the paucity of adjustable parameters. Scott De Vito ([1997]) charges that these solutions are 'conventional' because he thinks that the number of adjustable parameters may change when the hypotheses are described differently. This he believes is exactly what is illustrated in Goodman's new riddle of induction, otherwise known as the grue problem. However, the 'number of adjustable (...) parameters' is actually a loose way of referring to a quantity that is not language dependent. The quantity arises out of Akaike's theorem in a way that ensures its language invariance. (shrink)