Cluster analysis identifies homogeneous groups that are relevant within a population. In model-based clustering, group membership is estimated using a parametric finite mixture model, commonly the mathematically tractable Gaussian mixture model. One-way clustering methods can be restrictive in cases where there are suspected relationships between the variables in each component, leading to the idea of biclustering, which refers to clustering both observations and variables simultaneously. When the relationships between the variables are known, biclustering becomes one-way supervised. To this end, this thesis focuses on a novel one-way supervised biclustering family based on the Gaussian mixture model. In cases where biclustering may be overestimating the number of components in the data, a model averaging technique utilizing Occam's window is applied to produce better clustering results. Automatic outlier detection is introduced into the biclustering family using mixtures of contaminated Gaussian mixture models. Algorithms for model-fitting and parameter estimation are presented for the techniques described in this thesis, and simulation and real data studies are used to assess their performance. / Thesis / Doctor of Philosophy (PhD)

<p>This dissertation consists of three parts of empirical analyses investigating temporal patterns and consequences of (childhood) overweight and obesity, mainly in the United States and the People's Republic of China. Based on the China Health and Nutrition Survey, the first part conducts hierarchical age-period-cohort analyses of childhood overweight in China and finds a strong cohort effect driving the overweight epidemic. Results from the growth-curve models show that childhood overweight and underweight are related such that certain socio-economic groups with higher levels of childhood overweight also exhibit lower levels of childhood underweight. The second part situates the discussion on childhood obesity in a broader context. It compares temporal patterns of childhood overweight in China with these of adulthood overweight and finds that the salient cohort component is absent in rising adulthood overweight, which is dominated by strong period effects. A positive association between human development index and overweight/obesity prevalence across countries is also documented. Using multiple waves of survey data from the National Longitudinal Study of Adolescent Health, the third part analyzes the (latent) trajectory of childhood overweight/obesity in the United States. It finds that individuals with obesity growth trajectories are less likely to avoid mental depression, tend to have higher levels of neuroticism and lower levels of agreeableness/conscientiousness, and show less delinquent behaviors.</p> / Dissertation

In the present paper we discuss Bayesian estimation of a very general model class where the distribution of the observations is assumed to depend on a latent mixture or switching variable taking values in a discrete state space. This model class covers e.g. finite mixture modelling, Markov switching autoregressive modelling and dynamic linear models with switching. Joint Bayesian estimation of all latent variables, model parameters and parameters determining the probability law of the switching variable is carried out by a new Markov Chain Monte Carlo method called permutation sampling. Estimation of switching and mixture models is known to be faced with identifiability problems as switching and mixture are identifiable only up to permutations of the indices of the states. For a Bayesian analysis the posterior has to be constrained in such a way that identifiablity constraints are fulfilled. The permutation sampler is designed to sample efficiently from the constrained posterior, by first sampling from the unconstrained posterior - which often can be done in a convenient multimove manner - and then by applying a suitable permutation, if the identifiability constraint is violated. We present simple conditions on the prior which ensure that this method is a valid Markov Chain Monte Carlo method (that is invariance, irreducibility and aperiodicity hold). Three case studies are presented, including finite mixture modelling of fetal lamb data, Markov switching Autoregressive modelling of the U.S. quarterly real GDP data, and modelling the U .S./U.K. real exchange rate by a dynamic linear model with Markov switching heteroscedasticity. (author's abstract) / Series: Forschungsberichte / Institut für Statistik

Finite mixture models have had a profound impact on the history of statistics, contributing to modelling heterogeneous populations, generalizing distributional assumptions, and lately, presenting a convenient framework for classification and clustering. A novel approach, via Gaussian mixture distribution, is introduced for modelling receiver operating characteristic curves. The absence of a closed-form for a functional form leads to employing the Monte Carlo method. This approach performs excellently compared to the existing methods when applied to real data. In practice, the data are often non-normal, atypical, or skewed. It is apparent that non-Gaussian distributions be introduced in order to better fit these data. Two non-Gaussian mixtures, i.e., t distribution and skew t distribution, are proposed and applied to real data. A novel mixture is presented to cluster spatial and temporal data. The proposed model defines each mixture component as a mixture of autoregressive polynomial with logistic links. The new model performs significantly better compared to the most well known model-based clustering techniques when applied to real data. / Thesis / Doctor of Philosophy (PhD)

Growth mixture models (GMMs) are used to model intra-individual change and inter-individual differences in change and to detect underlying group structure in longitudinal studies. Regularly, these models are fitted under the assumption of normality, an assumption that is frequently invalid. To this end, this thesis focuses on the development of novel non-elliptical growth mixture models to better fit real data. Two non-elliptical growth mixture models, via the multivariate skew-t distribution and the generalized hyperbolic distribution, are developed and applied to simulated and real data. Furthermore, these two non-elliptical growth mixture models are extended to accommodate missing values, which are near-ubiquitous in real data. Recently, finite mixtures of non-elliptical distributions have flourished and facilitated the flexible clustering of the data featuring longer tails and asymmetry. However, in practice, real data often have missing values, and so work in this direction is also pursued. A novel approach, via mixtures of the generalized hyperbolic distribution and mixtures of the multivariate skew-t distributions, is presented to handle missing values in mixture model-based clustering context. To increase parsimony, families of mixture models have been developed by imposing constraints on the component scale matrices whenever missing data occur. Next, a mixture of generalized hyperbolic factor analyzers model is also proposed to cluster high-dimensional data with different patterns of missing values. Two missingness indicator matrices are also introduced to ease the computational burden. The algorithms used for parameter estimation are presented, and the performance of the methods is illustrated on simulated and real data. / Thesis / Doctor of Philosophy (PhD)

Finite mixture modelling is a powerful and well-developed paradigm, having proven useful in unsupervised learning and, to a lesser extent supervised learning (mixture discriminant analysis), especially in the case(s) of data with local variation and/or latent variables. It is the aim of this thesis to improve upon mixture discriminant analysis by introducing two types of random forest analogues which are called Mix- Forests. The first MixForest is based on Gaussian mixture models from the famous family of Gaussian parsimonious clustering models and will be useful in classify- ing lower dimensional data. The second MixForest extends the technique to higher dimensional data via the use of mixtures of factor analyzers from the well-known family of parsimonious Gaussian mixture models. MixForests will be utilized in the analysis of real data to demonstrate potential increases in classification accuracy as well as inferential procedures such as generalization error estimation and variable importance measures. / Thesis / Doctor of Philosophy (PhD)

In this dissertation, first we consider the problem of testing homogeneity and order in a contaminated normal model, when the data is correlated under some known covariance structure. To address this problem, we developed a moment based homogeneity and order test, and design weights for test statistics to increase power for homogeneity test. We applied our test to microarray about Down’s syndrome. This dissertation also studies a singular Bayesian information criterion (sBIC) for a bivariate hierarchical mixture model with varying weights, and develops a new data dependent information criterion (sFLIC).We apply our model and criteria to birth- weight and gestational age data for the same model, whose purposes are to select model complexity from data.

This thesis consists of three self-contained essays about absenteeism. Essay I analyzes if the design of the insurance system affects work absence, i.e. the classic insurance problem of moral hazard. Several reforms of the sickness insurance system were implemented during the period 1991-1996. Using Negative binomial models with fixed effects, the analysis show that both workers and employers changed their behavior due to the reforms. We also find that the extent of moral hazard varies depending on work contract structures. The reforms reducing the compensation levels decreased workers’ absence, both the number of absent days and the number of absence spells. The reform in 1992, introducing sick pay paid by the employers, also decreased absence levels, which probably can be explained by changes in personnel policy such as increased use of monitoring and screening of workers. Essay II examines the background to gender differences in work absence. Women are found, as in many earlier studies, to have higher absence levels than men. Our analysis, using finite mixture models, reveals that there are a group of women, comprised of about 41% of the women in our sample, that have a high average demand of absence. Among men, the high demand group is smaller consisting of about 36% of the male sample. The absence behavior differs as much between groups within gender as it does between men and women. The access to panel data covering the period 1971-1991 enables an analysis of the increased gender gap over time. Our analysis shows that the increased gender gap can be attributed to changes in behavior rather than in observable characteristics. Essay III analyzes the difference in work absence between natives and immigrants. Immigrants are found to have higher absence than natives when measured as the number of absent days. For the number of absence spells, the pattern for immigrants and natives is about the same. The analysis, using panel data and count data models, show that natives and immigrants have different characteristics concerning family situation, work conditions and health. We also find that natives and immigrants respond differently to these characteristics. We find, for example, that the absence of natives and immigrants are differently related to both economic incentives and work environment. Finally, our analysis shows that differences in work conditions and work environment only can explain a minor part of the ethnic differences in absence during the 1980’s.

[EN] This thesis considers new applications of non-Gaussian mixtures in the framework of statistical signal processing and pattern recognition. The non-Gaussian mixtures were implemented by mixtures of independent component analyzers (ICA). The fundamental hypothesis of ICA is that the observed signals can be expressed as a linear transformation of a set of hidden variables, usually referred to as sources, which are statistically independent. This independence allows factoring the original M-dimensional probability density function (PDF) of the data as a product of one-dimensional probability densities, greatly simplifying the modeling of the data. ICA mixture models (ICAMM) provide further flexibility by alleviating the independency requirement of ICA, thus allowing the model to obtain local projections of the data without compromising its generalization capabilities. Here are explored new possibilities of ICAMM for the purposes of estimation and classification of signals. The thesis makes several contributions to the research in non-Gaussian mixtures: (i) a method for maximum-likelihood estimation of missing data, based on the maximization of the PDF of the data given the ICAMM; (ii) a method for Bayesian estimation of missing data that minimizes the mean squared error and can obtain the confidence interval of the prediction; (iii) a generalization of the sequential dependence model for ICAMM to semi-supervised or supervised learning and multiple chains of dependence, thus allowing the use of multimodal data; and (iv) introduction of ICAMM in diverse novel applications, both for estimation and for classification. The developed methods were validated via an extensive number of simulations that covered multiple scenarios. These tested the sensitivity of the proposed methods with respect to the following parameters: number of values to estimate; kinds of source distributions; correspondence of the data with respect to the assumptions of the model; number of classes in the mixture model; and unsupervised, semi-supervised, and supervised learning. The performance of the proposed methods was evaluated using several figures of merit, and compared with the performance of multiple classical and state-of-the-art techniques for estimation and classification. Aside from the simulations, the methods were also tested on several sets of real data from different types: data from seismic exploration studies; ground penetrating radar surveys; and biomedical data. These data correspond to the following applications: reconstruction of damaged or missing data from ground-penetrating radar surveys of historical walls; reconstruction of damaged or missing data from a seismic exploration survey; reconstruction of artifacted or missing electroencephalographic (EEG) data; diagnosis of sleep disorders; modeling of the brain response during memory tasks; and exploration of EEG data from subjects performing a battery of neuropsychological tests. The obtained results demonstrate the capability of the proposed methods to work on problems with real data. Furthermore, the proposed methods are general-purpose and can be used in many signal processing fields. / [ES] Esta tesis considera nuevas aplicaciones de las mezclas no Gaussianas dentro del marco de trabajo del procesado estadístico de señal y del reconocimiento de patrones. Las mezclas no Gaussianas fueron implementadas mediante mezclas de analizadores de componentes independientes (ICA). La hipótesis fundamental de ICA es que las señales observadas pueden expresarse como una transformación lineal de un grupo de variables ocultas, normalmente llamadas fuentes, que son estadísticamente independientes. Esta independencia permite factorizar la función de densidad de probabilidad (PDF) original M-dimensional de los datos como un producto de densidades unidimensionales, simplificando ampliamente el modelado de los datos. Los modelos de mezclas ICA (ICAMM) aportan una mayor flexibilidad al relajar el requisito de independencia de ICA, permitiendo que el modelo obtenga proyecciones locales de los datos sin comprometer su capacidad de generalización. Aquí se exploran nuevas posibilidades de ICAMM para los propósitos de estimación y clasificación de señales. La tesis realiza varias contribuciones a la investigación en mezclas no Gaussianas: (i) un método de estimación de datos faltantes por máxima verosimilitud, basado en la maximización de la PDF de los datos dado el ICAMM; (ii) un método de estimación Bayesiana de datos faltantes que minimiza el error cuadrático medio y puede obtener el intervalo de confianza de la predicción; (iii) una generalización del modelo de dependencia secuencial de ICAMM para aprendizaje supervisado o semi-supervisado y múltiples cadenas de dependencia, permitiendo así el uso de datos multimodales; y (iv) introducción de ICAMM en varias aplicaciones novedosas, tanto para estimación como para clasificación. Los métodos desarrollados fueron validados mediante un número extenso de simulaciones que cubrieron múltiples escenarios. Éstos comprobaron la sensibilidad de los métodos propuestos con respecto a los siguientes parámetros: número de valores a estimar; tipo de distribuciones de las fuentes; correspondencia de los datos con respecto a las suposiciones del modelo; número de clases en el modelo de mezclas; y aprendizaje supervisado, semi-supervisado y no supervisado. El rendimiento de los métodos propuestos fue evaluado usando varias figuras de mérito, y comparado con el rendimiento de múltiples técnicas clásicas y del estado del arte para estimación y clasificación. Además de las simulaciones, los métodos también fueron probados sobre varios grupos de datos de diferente tipo: datos de estudios de exploración sísmica; exploraciones por radar de penetración terrestre; y datos biomédicos. Estos datos corresponden a las siguientes aplicaciones: reconstrucción de datos dañados o faltantes de exploraciones de radar de penetración terrestre de muros históricos; reconstrucción de datos dañados o faltantes de un estudio de exploración sísmica; reconstrucción de datos electroencefalográficos (EEG) dañados o artefactados; diagnóstico de desórdenes del sueño; modelado de la respuesta del cerebro durante tareas de memoria; y exploración de datos EEG de sujetos durante la realización de una batería de pruebas neuropsicológicas. Los resultados obtenidos demuestran la capacidad de los métodos propuestos para trabajar en problemas con datos reales. Además, los métodos propuestos son de propósito general y pueden utilizarse en muchos campos del procesado de señal. / [CA] Aquesta tesi considera noves aplicacions de barreges no Gaussianes dins del marc de treball del processament estadístic de senyal i del reconeixement de patrons. Les barreges no Gaussianes van ser implementades mitjançant barreges d'analitzadors de components independents (ICA). La hipòtesi fonamental d'ICA és que els senyals observats poden ser expressats com una transformació lineal d'un grup de variables ocultes, comunament anomenades fonts, que són estadísticament independents. Aquesta independència permet factoritzar la funció de densitat de probabilitat (PDF) original M-dimensional de les dades com un producte de densitats de probabilitat unidimensionals, simplificant àmpliament la modelització de les dades. Els models de barreges ICA (ICAMM) aporten una major flexibilitat en alleugerar el requeriment d'independència d'ICA, permetent així que el model obtinga projeccions locals de les dades sense comprometre la seva capacitat de generalització. Ací s'exploren noves possibilitats d'ICAMM pels propòsits d'estimació i classificació de senyals. Aquesta tesi aporta diverses contribucions a la recerca en barreges no Gaussianes: (i) un mètode d'estimació de dades faltants per màxima versemblança, basat en la maximització de la PDF de les dades donat l'ICAMM; (ii) un mètode d'estimació Bayesiana de dades faltants que minimitza l'error quadràtic mitjà i pot obtenir l'interval de confiança de la predicció; (iii) una generalització del model de dependència seqüencial d'ICAMM per entrenament supervisat o semi-supervisat i múltiples cadenes de dependència, permetent així l'ús de dades multimodals; i (iv) introducció d'ICAMM en diverses noves aplicacions, tant per a estimació com per a classificació. Els mètodes desenvolupats van ser validats mitjançant una extensa quantitat de simulacions que cobriren múltiples situacions. Aquestes van verificar la sensibilitat dels mètodes proposats amb respecte als següents paràmetres: nombre de valors per estimar; mena de distribucions de les fonts; correspondència de les dades amb respecte a les suposicions del model; nombre de classes del model de barreges; i aprenentatge supervisat, semi-supervisat i no-supervisat. El rendiment dels mètodes proposats va ser avaluat mitjançant diverses figures de mèrit, i comparat amb el rendiments de múltiples tècniques clàssiques i de l'estat de l'art per a estimació i classificació. A banda de les simulacions, els mètodes van ser verificats també sobre diversos grups de dades reals de diferents tipus: dades d'estudis d'exploració sísmica; exploracions de radars de penetració de terra; i dades biomèdiques. Aquestes dades corresponen a les següents aplicacions: reconstrucció de dades danyades o faltants d'estudis d'exploracions de radar de penetració de terra sobre murs històrics; reconstrucció de dades danyades o faltants en un estudi d'exploració sísmica; reconstrucció de dades electroencefalogràfiques (EEG) artefactuades o faltants; diagnosi de desordres de la son; modelització de la resposta del cervell durant tasques de memòria; i exploració de dades EEG de subjectes realitzant una bateria de tests neuropsicològics. Els resultats obtinguts han demostrat la capacitat dels mètodes proposats per treballar en problemes amb dades reals. A més, els mètodes proposats són de propòsit general i poden fer-se servir en molts camps del processament de senyal. / Safont Armero, G. (2015). New Insights in Prediction and Dynamic Modeling from Non-Gaussian Mixture Processing Methods [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/53913

Esta tese se concentra em aplicar os modelos de mistura de distribuições na segmentação de imagens SAR polarimétricas multi-look. Dentro deste contexto, utilizou-se o algoritmo SEM em conjunto com os estimadores obtidos pelo método dos momentos para calcular as estimativas dos parâmetros do modelo de mistura das distribuições Wishart, Kp ou G0p. Cada uma destas distribuições possui parâmetros específicos que as diferem no ajuste dos dados com graus de homogeneidade variados. A distribuição Wishart descreve bem regiões com características mais homogêneas, como cultivo. Esta distribuição é muito utilizada na análise de dados SAR polarimétricos multi-look. As distribuições Kp e G0p possuem um parâmetro de rugosidade que as permitem descrever tanto regiões mais heterogêneas, como vegetação e áreas urbanas, quanto regiões homogêneas. Além dos modelos de mistura de uma única família de distribuições, também foi analisado o caso de um dicionário contendo as três famílias. Há comparações do método SEM proposto para os diferentes modelos com os métodos da literatura k-médias e EM utilizando imagens reais da banda L. O método SEM com a mistura de distribuições G0p forneceu os melhores resultados quando os outliers da imagem são desconsiderados. A distribuição G0p foi a mais flexível ao ajuste dos diferentes tipos de alvo. A distribuição Wishart foi robusta às diferentes inicializações. O método k-médias com a distribuição Wishart é robusto à segmentação de imagens contendo outliers, mas não é muito flexível à variabilidade das regiões heterogêneas. O modelo de mistura do dicionário de famílias melhora a log-verossimilhança do método SEM, mas apresenta resultados parecidos com os do modelo de mistura G0p. Para todos os tipos de inicialização e grupos, a distribuição G0p predominou no processo de seleção das distribuições do dicionário de famílias. / The main focus of this thesis consists of the application of mixture models in multi-look polarimetric SAR image segmentation. Within this context, the SEM algorithm, together with the method of moments, were applied in the estimation of the Wishart, Kp and G0p mixture model parameters. Each one of these distributions has specific parameters that allows fitting data with different degrees of homogeneity. The Wishart distribution is suitable for modeling homogeneous regions, like crop fields for example. This distribution is widely used in multi-look polarimetric SAR data analysis. The distributions Kp and G0p have a roughness parameter that allows them to describe both heterogeneous regions, as vegetation and urban areas, and homogeneous regions. Besides adopting mixture models of a single family of distributions, the use of a dictionary with all the three family of distributions was proposed and analyzed. Also, a comparison between the performance of the proposed SEM method, considering the different models in real L-band images and two widely known techniques described in literature (k-means and EM algorithms), are shown and discussed. The proposed SEM method, considering a G0p mixture model combined with a outlier removal stage, provided the best classication results. The G0p distribution was the most flexible for fitting the different kinds of data. The Wishart distribution was robust for different initializations. The k-means algorithm with Wishart distribution is robust for segmentation of SAR images containing outliers, but it is not so flexible to variabilities in heterogeneous regions. The mixture model considering the dictionary of distributions improves the SEM method log-likelihood, but presents similar results to those of G0p mixture model. For all types of initializations and clusters, the G0p prevailed in the distribution selection process of the dictionary of distributions.