An introduction to the imprecise Dirichlet model for multinomial data
International Journal of Approximate Reasoning
Estimation of Constrained Parameters With Guaranteed MSE Improvement
IEEE Transactions on Signal Processing
Inference with multinomial data: why to weaken the prior strength
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Three
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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].