Dirichlet or Potts - Physics > Data Analysis, Statistics and ProbabilityReport as inadecuate

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Abstract: When modeling the distribution of a set of data by a mixture of Gaussians,there are two possibilities: i) the classical one is using a set of parameterswhich are the proportions, the means and the variances; ii) the second is toconsider the proportions as the probabilities of a discrete valued hiddenvariable. In the first case a usual prior distribution for the proportions isthe Dirichlet which accounts for the fact that they have to sum up to one. Inthe second case, to each data is associated a hidden variable for which weconsider two possibilities: a) assuming those variables to be i.i.d. We showthen that this scheme is equivalent to the classical mixture model withDirichlet prior; b) assuming a Markovian structure. Then we choose the simplestmarkovian model which is the Potts distribution. As we will see this model ismore appropriate for the case where the data represents the pixels of an imagefor which the hidden variables represent a segmentation of that image. The mainobject of this paper is to give some details on these models and differentalgorithms used for their simulation and the estimation of their parameters.Key Words: Mixture of Gaussians, Dirichlet, Potts, Classification,Segmentation.

Author: Ali Mohammad-Djafari

Source: https://arxiv.org/

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