The curve fitting problem: A Bayesian rejoinder

In the curve fitting problem two conflicting desiderata, simplicity and goodness-of-fit pull in opposite directions. To solve this problem, two proposals, the first one based on Bayes's theorem criterion (BTC) and the second one advocated by Forster and Sober based on Akaike's Information Criterion (AIC) are discussed. We show that AIC, which is frequentist in spirit, is logically equivalent to ETC, provided that a suitable choice of priors is made. We evaluate the charges against Bayesianism and contend that AIC approach has shortcomings. We also discuss the relationship between Schwan's Bayesian Information Criterion and ETC.