In our paper we recall some known mixture operators and their properties. We introduce sufficient conditions for weighting functions to ensure the monotonicity of the corresponding operators. We introduce new applications of mixture operators in the insurance, namely in the additional insurance.

Abstract: Stochastic models such as mixture models, graphical models, Markov random fields and hidden Markov models have key role in probabilistic data analysis. In this paper, we used Gaussian mixture model to the pixels of an image. The parameters of the model were estimated by EM-algorithm.   In addition pixel labeling corresponded to each pixel of true image was made by Bayes rule. In fact,...

The mixture Rasch model is a popular for analyzing multivariate binary data. drawback of this that the number estimated parameters substantially increases with an increasing latent classes, which, in turn, hinders interpretability parameters. This article proposes regularized estimation imposes some sparsity structure on class-specific item difficulties. We illustrate feasibility proposed model...

1 Variational Dirichlet Process mixtures Assume two infinite sets φ = {φ1, φ2, . . .} and v = {v1, v2, . . . , } of component parameter vectors and beta distributed random variables. Each φk is independently drawn from the prior pφ(φk|λ) with hyperparameter λ and each vk is independently drawn from B(vk|1, α) with hyperparameter α. Given these sets a Dirichlet Process (DP) mixture model is writ...

Figure 1: Bayesian Mixture Model For a Bayesian Mixture Model as shown in figure 1, as k →∞, we shall have G = ∑∞ c=1 πcδφc , where all the φc are i.i.d. samples from G0, while the random sequence {πc}c=1 sum up to one, shall be constructed by the “Stick Breaking” process [3]. Suppose there is a stick with length 1. Let βc ∼ Beta(1, α) for c = 1, 2, 3, . . . , and regard them as fractions we ta...