Inference from Multinomial Data Based on a MLE-Dominance Criterion

  • Alessio Benavoli
  • Cassio P. de Campos
Conference paper

DOI: 10.1007/978-3-642-02906-6_4

Part of the Lecture Notes in Computer Science book series (LNCS, volume 5590)
Cite this paper as:
Benavoli A., de Campos C.P. (2009) Inference from Multinomial Data Based on a MLE-Dominance Criterion. In: Sossai C., Chemello G. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2009. Lecture Notes in Computer Science, vol 5590. Springer, Berlin, Heidelberg

Abstract

We consider the problem of inference from multinomial data with chances \(\boldsymbol{\theta}\), subject to the a-priori information that the true parameter vector \(\boldsymbol{\theta}\) belongs to a known convex polytope \(\boldsymbol{\Theta}\). The proposed estimator has the parametrized structure of the conditional-mean estimator with a prior Dirichlet distribution, whose parameters (s,t) are suitably designed via a dominance criterion so as to guarantee, for any \(\boldsymbol{\theta} \in \boldsymbol{\Theta}\), an improvement of the Mean Squared Error over the Maximum Likelihood Estimator (MLE). The solution of this MLE-dominance problem allows us to give a different interpretation of: (1) the several Bayesian estimators proposed in the literature for the problem of inference from multinomial data; (2) the Imprecise Dirichlet Model (IDM) developed by Walley [13].

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Alessio Benavoli
    • 1
  • Cassio P. de Campos
    • 1
  1. 1.Dalle Molle Institute for Artificial IntelligenceMannoSwitzerland

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