@CONFERENCE\{IMM2000-04834,
author = "L. K. Hansen",
title = "Bayesian Averaging is Well-Temperated",
year = "2000",
pages = "265-271",
booktitle = "Advances in Neural Information Processing Systems 1999",
volume = "",
series = "",
editor = "S. Solla et al.",
publisher = "{MIT} Press",
organization = "",
address = "",
url = "http://www2.imm.dtu.dk/pubdb/p.php?4834",
abstract = "Bayesian predictions are stochastic just like predictions of any other
inference scheme that generalize from a finite sample. While a simple variational argument shows that Bayes averaging is generalization optimal given that the prior matches the teacher parameter distribution the situation is less clear if the teacher distribution is unknown. I define a class of averaging procedures, the temperated likelihoods, including both Bayes averaging with a uniform prior and maximum likelihood estimation as special cases. I show that
Bayes is generalization optimal in this family for any teacher distribution for two learning problems that are analytically tractable learning the mean of a Gaussian and asymptotics of smooth learners."
}