In this paper, we show how Gibbs sampling can provide a reliable approximation for Bayesian estimation of the parameters of a mixture distribution. Moreover, we deduce from the Bayesian approach an alternative derivation of maximum likelihood estimators in this setting, where standard nonin-formative approaches do not apply. Our method uses conjugate priors on each component of the mixture and is called Prior Feedback because the hyperparameters of these conjugate priors are iteratively replaced by the cor-responding posterior values until convergence is attained. We illustrate the appeal of this method through an astrophysical example, where the small sample size prohibits the use of standard maximum likelihood methods. A second example shows that Prior Feedback is also able to reject an unrealistic mixture model.
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