Title: A Noninformative Prior on a Space of Distribution Functions,
Abstract: In a given problem, the Bayesian statistical paradigm requires the
specification of a prior distribution that quantifies relevant information
about the unknowns of main interest external to the data. In cases where little
such information is available, the problem under study may possess an
invariance under a transformation group that encodes a lack of information,
leading to a unique prior---this idea was explored at length by E.T. Jaynes.
Previous successful examples have included location-scale invariance under
linear transformation, multiplicative invariance of the rate at which events in
a counting process are observed, and the derivation of the Haldane prior for a
Bernoulli success probability. In this paper we show that this method can be
extended, by generalizing Jaynes, in two ways: (1) to yield families of
approximately invariant priors, and (2) to the infinite-dimensional setting,
yielding families of priors on spaces of distribution functions. Our results
can be used to describe conditions under which a particular Dirichlet Process
posterior arises from an optimal Bayesian analysis, in the sense that
invariances in the prior and likelihood lead to one and only one posterior
distribution.