Abstract
The specification of a prior distribution on the set of all distribution functions permits to consider a non parametric bayesian experiment as an abstract probability space on which are defined the sampling process and a stochastic distribution process.
In this framework, the Dirichlet process may be characterized, in several ways, in terms of one-dimensional distributions and independence relations between associated σ-algebras. These independence relations naturally define extensions of the Dirichlet process called neutral processes. The power of this approach may be appreciated in three ways. It significantly simplifies the computation of the posterior distribution, it gives new characterizations of the Dirichlet process, and finally it solves Docksum’s conjecture that the only distribution process that is both neutral to the right and neutral to the left is the Dirichlet process.
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© 1983 Springer-Verlag New York Inc.
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Rolin, J.M. (1983). Non Parametric Bayesian Statistics: A Stochastic Process Approach. In: Florens, J.P., Mouchart, M., Raoult, J.P., Simar, L., Smith, A.F.M. (eds) Specifying Statistical Models. Lecture Notes in Statistics, vol 16. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-5503-1_8
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DOI: https://doi.org/10.1007/978-1-4612-5503-1_8
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