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An up-to-date, comprehensive account of major issues in finite mixture modeling This volume provides an up-to-date account of the theory and applications of modeling via finite mixture distributions. With an emphasis on the applications of mixture models in both mainstream analysis and other areas such as unsupervised pattern recognition, speech recognition, and medical imaging, the book describes the formulations of the finite mixture approach, details its methodology, discusses aspects of its implementation, and illustrates its application in many common statistical contexts

Finite mixture distributions are a weighted average of a ¯nite number of distributions. The latter are usually called the mixture components. The weights are usually described by a multinomial distribution and are sometimes called mixing proportions. The mixture components may be the same type of distributions with di®erent parameter values but they may also be completely di®erent distributions (Everitt and Hand, 1981; Titterington et al., 1985). Therefore, ¯nite mixture distributions are very °exible for modeling data. They are frequently used as a building block within many modern econometric models. The speci¯cation of the mixture distribution depends on the modeling problem at hand. In this thesis, we introduce new applications of ¯nite mixtures to deal with several di®erent modeling issues. Each chapter of the thesis focusses on a speci¯c modeling issue. The parameters of some of the resulting models can be estimated using standard techniques but for some of the chapters we need to develop new estimation and inference methods. To illustrate how the methods can be applied, we analyze at least one empirical data set for each approach. These data sets cover a wide range of research ¯elds, such as macroeconomics, marketing, and political science. We show the usefulness of the methods and, in some cases, the improvement over previous methods in the literature.

The standard mixture model, the concomitant variable mixture model, the mixture regression model and the concomitant variable mixture regression model all enable simultaneous identification and description of groups of observations. This study reviews the different ways in which dependencies among the variables involved in these models are accommodated. It is demonstrated that the standard and concomitant variable mixture models identify groups of observations and at the same time discriminate them analogous, respectively, to discriminant analysis and logistic regression. While the mixture regression model is shown to have limited use for classifying new observations. An extension of it, called the saturated mixture regression model, is shown to be more useful in that respect. Advantages of that model in model estimation when missing data are present and as a framework for model selection are also discussed.

[EN] In this work, we propose a new Bayesian model for unsupervised image segmentation based on a combination of the spatially varying finite mixture models (SVFMMs) and the non-local means (NLM) framework. The probabilistic NLM weighting function is successfully integrated into a varying Gauss¿Markov random field, yielding a prior density that adaptively imposes a local regularization to simultaneously preserve edges and enforce smooth constraints in homogeneous regions of the image. Two versions of our model are proposed: a pixel-based model and a patch-based model, depending on the design of the probabilistic NLM weighting function. Contrary to previous methods proposed in the literature, our approximation does not introduce new parameters to be estimated into the model, because the NLM weighting function is completely known once the neighborhood of a pixel is fixed. The proposed model can be estimated in closed-form solution via a maximum a posteriori (MAP) estimation in an expectation¿maximization scheme. We have compared our model with previously proposed SVFMMs using two public datasets: the Berkeley Segmentation dataset and the BRATS 2013 dataset. The proposed model performs favorably to previous approaches in the literature, achieving better results in terms of Rand Index and Dice metrics in our experiments. ; This study is partially supported by Secretaria de Estado de Investigacion, Desarrollo e Innovacion (DPI2016-80054-R, TIN2013-43457-R) and Agencia Valenciana de la Innovacion (INNVAL10/18/048). E.F.G was supported by the European Union's Horizon 2020 research and innovation programme under the Marie Skodowska-Curie grant agreement (No. 844646) and also acknowledges the support of NVIDIA GPU Grant Program. ; Juan -Albarracín, J.; Fuster García, E.; Juan, A.; Garcia-Gomez, JM. (2021). Non-local spatially varying finite mixture models for image segmentation. Statistics and Computing. 31(1):1-10. https://doi.org/10.1007/s11222-020-09988-w ; S ; 1 ; 10 ; 31 ; 1

306 318 262 ; S ; Nuclear Power Plant safety analysis is mainly based on the use of best estimate (BE) codes that predict the plant behavior under normal or accidental conditions. As the BE codes introduce uncertainties due to uncertainty in input parameters and modeling, it is necessary to perform uncertainty assessment (UA), and eventually sensitivity analysis (SA), of the results obtained. These analyses are part of the appropriate treatment of uncertainties imposed by current regulation based on the adoption of the best estimate plus uncertainty (BEPU) approach. The most popular approach for uncertainty assessment, based on Wilks' method, obtains a tolerance/confidence interval, but it does not completely characterize the output variable behavior, which is required for an extended UA and SA. However, the development of standard UA and SA impose high computational cost due to the large number of simulations needed. In order to obtain more information about the output variable and, at the same time, to keep computational cost as low as possible, there has been a recent shift toward developing metamodels (model of model), or surrogate models, that approximate or emulate complex computer codes. In this way, there exist different techniques to reconstruct the probability distribution using the information provided by a sample of values as, for example, the finite mixture models. In this paper, the Expectation Maximization and the k-means algorithms are used to obtain a finite mixture model that reconstructs the output variable probability distribution from data obtained with RELAP-5 simulations. Both methodologies have been applied to a separated effects experiment, and to an integral effects simulation. This work has been partially supported by the Consejo de Seguridad Nuclear under the contract with reference STN/2369/08/640. Carlos Alberola, S.; Sánchez Galdón, AI.; Ginestar Peiro, D.; Martorell Alsina, SS. (2013). Using finite mixture models in thermal-hydraulics system code uncertainty analysis. Nuclear ...

When are individuals more likely to support immigration? We suggest here that regional international organizations (IOs; for example, the European Union) publicly release reports about the scale and benefits of immigration to member states in the region in which these IOs operate. We argue that unlike individuals who are uninformed about immigration, informed individuals who have more knowledge of the main regional IO in which their country participates will be more likely to employ immigration reports released by their regional IO to construct their immigration attitudes. They will also perceive that these reports are credible. The credibility of these reports helps individuals with more knowledge about their region's main IO to view immigrants favorably, which translates to support for immigration. We test our prediction by developing a finite mixture model that statistically accounts for the econometric challenges that emerge when uninformed individuals "save face" by disproportionately opting for the middle "status quo" category in ordinal survey response variables of immigration support. Results from the finite mixture model corroborate our prediction and are more reliable than estimates from a standard ordered probit model. (International Interactions (London)/ FUB)