Abstract

This paper introduces a scheme for constructing prior distributions on a space of probability measures using a tree of exchangeable processes. The exchangeable tree scheme provides a natural generalization of the Polya tree priors presented by Mauldin et al. (1992). Exchangeable tree priors provide useful conjugate families of priors for statistical models in which an experiment proceeds in several stages with each stage dependent on the previous outcomes. The exchangeable tree construction has some advantages over other constructions. For instance, exchangeable tree priors can give probability one to the set of continuous measures unlike, say, Dirichlet processes. Moreover, the scheme’s perspective is both a conceptual aid in sampling applications and a useful tool in deriving properties of the priors. The exchangeable tree scheme also gives an alternate way of constructing the random rescaling priors defined by Graf et al. (1986) and more generally by Mauldin and Monticino (1995). Here, some basic properties of exchangeable tree priors are developed and connections with other schemes – in particular, with random rescaling – for constructing priors are established.

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