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Expression explicite de l'évidence pour l'estimation du nombre de composantes d'un mélange de gaussiennes : cas particulier d'un petit nombre d'observations

Abstract : In this paper, we present a direct approach to select the number of components of a Gaussian mixture by computing the evidence. The joint distribution of the observations and the mixture parameters is written considering a Bayesian framework. Then, this quantity is marginalized over the mixture parameters in order to express the evidence. The choice of prior conjugate distributions makes it possible to compute the closed-form. Our approach is hence compared to the Bayesian Information Criterion (BIC) and the harmonic mean and its interest is shown more specifically for small data sets.
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https://hal.archives-ouvertes.fr/hal-01722787
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  • HAL Id : hal-01722787, version 1

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Jessica Sodjo, Audrey Giremus, Jean-François Giovannelli. Expression explicite de l'évidence pour l'estimation du nombre de composantes d'un mélange de gaussiennes : cas particulier d'un petit nombre d'observations. Colloque GRETSI, Sep 2015, Lyon, France. ⟨hal-01722787⟩

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