MischungModellen
MischungModellen refer to a family of probabilistic models that express the observed data as arising from a mixture of underlying subpopulations. Each subpopulation is represented by a probability distribution, and the overall distribution is a weighted sum of these components. The weights reflect the prevalence of each subpopulation. Finite MischungModellen assume a fixed number of components, while nonparametric variants allow the number of components to grow with the data.
Mathematical formulation: Given data x1, ..., xn, a finite MischungModell with K components has a density f(x)
Common components include Gaussian distributions (Gaussian Mischmodell Models), Poisson for count data, and more general exponential-family
Applications include clustering, density estimation, anomaly detection, and pattern recognition in fields such as genetics, finance,