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Exact Inference for Random Dirichlet Means

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Abstract

Two characterisations of a random mean from a Dirichlet process, as a limit of finite sums of a simple symmetric form and as a solution of a certain stochastic equation, are developed and investigated. These are used to reach results on and new insights into the distributions of such random means. In particular, identities involving functional transforms and recursive moment formulae are established. Furthermore, characterisations for several choices of the Dirichlet process parameter (leading to symmetric, unimodal, stable, and finite mixture distributions) are provided. Our methods lead to exact simulation recipes for prior and posterior random means, an approximation algorithm for the exact densities of these means, and limiting normality theorems for posterior distributions. The theory also extends to mixtures of Dirichlet processes and to the case of several random means simultaneously.

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Authors and Affiliations

  1. Department of Mathematics, University of Oslo, Italy

    Nils Lid Hjort

  2. Department of Statistics, University of Milano-Bicocca, Via Bicocca degli Arcimboldi 8, 20126, Milano, Italy

    Andrea Ongaro

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  1. Nils Lid Hjort
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  2. Andrea Ongaro
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Correspondence to Andrea Ongaro.

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Hjort, N.L., Ongaro, A. Exact Inference for Random Dirichlet Means. Stat Infer Stoch Process 8, 227–254 (2005). https://doi.org/10.1007/s11203-005-6068-7

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