Asymptotics of Continuous Bayes for Non-i.i.d. Sources

Abstract

Clarke and Barron analysed the relative entropy between an i.i.d. source and a Bayesian mixture over a continuous class containing that source. In this paper a comparable result is obtained when the source is permitted to be both non-stationary and dependent. The main theorem shows that Bayesian methods perform well for both compression and sequence prediction even in this most general setting with only mild technical assumptions.