The posterior distribution of the number of components k in a finite mixture satisfies a set of inequality constraints. The result holds irrespective of the parametric form of the mixture components and under assumptions on the prior distribution weaker than those routinely made in the literature on Bayesian analysis of finite mixtures. The inequality constraints can be used to perform an “inte...

Abstract. In this contribution, we present new algorithms to source separation for the case of noisy instantaneous linear mixture, within the Bayesian statistical framework. The source distribution prior is modeled by a mixture of Gaussians [1] and the mixing matrix elements distributions by a Gaussian [2]. We model the mixture of Gaussians hierarchically by mean of hidden variables representin...

The posterior distribution of the number of components k in a finite mixture satisfies a set of inequality constraints. The result holds irrespective of the parametric form of the mixture components and under assumptions on the prior distribution weaker than those routinely made in the literature on Bayesian analysis of finite mixtures. The inequality constraints can be used to perform an “inte...

Data with asymmetric heavy tails can arise from mixture of data from multiple populations or processes. We propose a computer intensive procedure to fit by quasi-maximum likelihood a mixture model to a robustly standardized data set. The robust standardization of the data set results in well defined tails which are modeled using extreme value theory. The data are assumed to be a mixture of a no...

-Maximum likelihood thresholding methods are presented on the basis of population mixture models. It turns out that the standard thresholding proposed by Otsu, which is based on a discriminant criterion and also minimizes the mean square errors between the original image and the resultant binary image, is equivalent to the maximization of the likelihood of the conditional distribution in the po...

This article considers the problem of evaluating infinite-time (or finite-time) ruin probability under a given compound Poisson surplus process by approximating the claim size distribution by a finite mixture exponential, say Hyperexponential, distribution. It restates the infinite-time (or finite-time) ruin probability as a solvable ordinary differential equation (or a partial differential equ...

I. MATHEMATICAL MODELS The mixture Weibull distribution produced from the combination has five or more parameters. These are; the shape parameters, scale parameters, location parameters, in addition to the mixing parameter (w). This type of distribution is even more useful because multiple causes of failure can be simultaneously modelled. Different values of the mixing parameter were used to ob...

This paper primarily is concerned with the sampling of the Fisher–Bingham distribution and we describe a slice sampling algorithm for doing this. A by-product of this task gave us an infinite mixture representation of the Fisher–Bingham distribution; the mixing distributions being based on the Dirichlet distribution. Finite numerical approximations are considered and a sampling algorithm based ...

You’ve collected the data and performed a preliminary analysis with a linear regression. But the residuals have several modes, and transformations don’t help. You need a different approach, and that calls for the FMM procedure. PROC FMM fits finite mixture models, which enable you to describe your data with mixtures of different distributions so you can account for underlying heterogeneity and ...

Variational Learning for Finite Inverted Dirichlet Mixture Models and Its Applications Parisa Tirdad Clustering is an important step in data mining, machine learning, computer vision and image processing. It is the process of assigning similar objects to the same subset. Among available clustering techniques, finite mixture models have been remarkably used, since they have the ability to consid...