This work considers a problem of estimating a mixing probability density in the setting of discrete mixture models. The paper consists of three parts. The first part focuses on the construction of an consistent estimator of . In particular, under the assumptions that the probability measure of the observation is atomic, and the map from to is bijective, it is shown that there exists an estimator such that for every density . The second part discusses the implementation details. Specifically, it is shown that the consistency for every can be attained with a computationally feasible estimator. The third part, as a study case, considers a Poisson mixture model. In particular, it is shown that in the Poisson noise setting, the bijection condition holds and, hence, estimation can be performed consistently for every .
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