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Journal of Statistical Theory and Practice

, Volume 9, Issue 3, pp 658–684 | Cite as

Imprecise Dirichlet Process With Application to the Hypothesis Test on the Probability That XY

  • Alessio Benavoli
  • Francesca Mangili
  • Fabrizio Ruggeri
  • Marco Zaffalon
Article

Abstract

The Dirichlet process (DP) is one of the most popular Bayesian nonparametric models. An open problem with the DP is how to choose its infinite-dimensional parameter (base measure) in case of lack of prior information. In this work, we present the imprecise DP (IDP)—a prior near-ignorance DP-based model that does not require any choice of this probability measure. It consists of a class of DPs obtained by letting the normalized base measure of the DP vary in the set of all probability measures. We discuss the tight connections of this approach with Bayesian robustness and in particular prior near-ignorance modeling via sets of probabilities. We use this model to perform a Bayesian hypothesis test on the probability P(XY). We study the theoretical properties of the IDP test (e.g., asymptotic consistency), and compare it with the frequentist Mann-Whitney-Wilcoxon rank test that is commonly employed as a test on P(XY). In particular, we show that our method is more robust, in the sense that it is able to isolate instances in which the aforementioned test is virtually guessing at random.

Keywords

Bayesian nonparametric test Imprecise Dirichlet process Wilcoxon rank sum 

AMS Subject Classification

62G10 62G35 

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Copyright information

© Grace Scientific Publishing 2015

Authors and Affiliations

  • Alessio Benavoli
    • 1
  • Francesca Mangili
    • 1
  • Fabrizio Ruggeri
    • 2
  • Marco Zaffalon
    • 1
  1. 1.IPG IDSIAMannoSwitzerland
  2. 2.CNR IMATIMilanoItaly

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