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Reliability analysis plays an important role in keeping manufacturers in a competitive position. It can be applied in many areas such as warranty predictions, maintenance scheduling, spare parts provisioning, and risk assessment. This dissertation focuses on statistical modeling and predictions based on lifetime data, degradation data, and recurrent event data. The datasets used in this dissertation come from the field, and have complicated structures. The dissertation consists of three main chapters, in addition to Chapter 1 which is the introduction chapter, and Chapter 5 which is the general conclusion chapter. Chapter 2 consists of the traditional time-to-failure data analysis. We propose a statistical method to address the failure data from an appliance used at home with the consideration of retirement times and delayed reporting time. We also develop a prediction method based on the proposed model. Using the information of retirement-time distribution and delayed reporting time, the predictions are more accurate and useful in the decision making. In Chapter 3, we introduce a nonlinear mixed-effects general path model to incorporate dynamic covariates into degradation data analysis. Dynamic covariates include time-varying environmental variables and usage condition. The shapes of the effect functions of covariates may be constrained to be, for example, monotonically increasing (i.e., higher temperature is likely to cause more damage). Incorporating dynamic covariates with shape restrictions is challenging. A modified alternative algorithm and the corresponding prediction method are proposed. In Chapter 4, we introduce a multi-level trend-renewal process (MTRP) model to describe component-level events in multi-level repairable systems. In particular, we consider two-level repairable systems in which events can occur at the subsystem level, or the component (within the subsystem) level. The main goal is to develop a method for estimation of model parameters and a procedure for prediction of the future replacement events at component level with the consideration of the effects from the subsystem replacement events. To explain unit-to-unit variability, time-dependent covariates as well as random effects are introduced into the heterogeneous MTRP model (HMTRP). A Metropolis-within-Gibbs algorithm is used to estimate the unknown parameters in the HMTRP model. The proposed method is illustrated by a simulated dataset. / Ph. D.

In longitudinal studies, data collected within a subject or cluster are somewhat correlated by their very nature and special cares are needed to account for such correlation in the analysis of data. Under the framework of longitudinal studies, three topics are being discussed in this thesis. In chapter 2, the joint modelling of multivariate longitudinal process consisting of different types of outcomes are discussed. In the large cohort study of UK north Stafforshire osteoarthritis project, longitudinal trivariate outcomes of continuous, binary and ordinary data are observed at baseline, year 3 and year 6. Instead of analysing each process separately, joint modelling is proposed for the trivariate outcomes to account for the inherent association by introducing random effects and the covariance matrix G. The influence of covariance matrix G on statistical inference of fixed-effects parameters has been investigated within the Bayesian framework. The study shows that by joint modelling the multivariate longitudinal process, it can reduce the bias and provide with more reliable results than it does by modelling each process separately. Together with the longitudinal measurements taken intermittently, a counting process of events in time is often being observed as well during a longitudinal study. It is of interest to investigate the relationship between time to event and longitudinal process, on the other hand, measurements taken for the longitudinal process may be potentially truncated by the terminated events, such as death. Thus, it may be crucial to jointly model the survival and longitudinal data. It is popular to propose linear mixed-effects models for the longitudinal process of continuous outcomes and Cox regression model for survival data to characterize the relationship between time to event and longitudinal process, and some standard assumptions have been made. In chapter 3, we try to investigate the influence on statistical inference for survival data when the assumption of mutual independence on random error of linear mixed-effects models of longitudinal process has been violated. And the study is conducted by utilising conditional score estimation approach, which provides with robust estimators and shares computational advantage. Generalised sufficient statistic of random effects is proposed to account for the correlation remaining among the random error, which is characterized by the data-driven method of modified Cholesky decomposition. The simulation study shows that, by doing so, it can provide with nearly unbiased estimation and efficient statistical inference as well. In chapter 4, it is trying to account for both the current and past information of longitudinal process into the survival models of joint modelling. In the last 15 to 20 years, it has been popular or even standard to assume that longitudinal process affects the counting process of events in time only through the current value, which, however, is not necessary to be true all the time, as recognised by the investigators in more recent studies. An integral over the trajectory of longitudinal process, along with a weighted curve, is proposed to account for both the current and past information to improve inference and reduce the under estimation of effects of longitudinal process on the risk hazards. A plausible approach of statistical inference for the proposed models has been proposed in the chapter, along with real data analysis and simulation study.

Les logiciels utilisés sont Splus et R. / Résumé La technique connue comme l'imputation multiple semble être la technique la plus appropriée pour résoudre le problème de non-réponse. La littérature mentionne des méthodes qui modélisent la nature et la structure des valeurs manquantes. Une des méthodes les plus populaires est l'algorithme « Pan » de (Schafer & Yucel, 2002). Les imputations rapportées par cette méthode sont basées sur un modèle linéaire multivarié à effets mixtes pour la variable réponse. La méthode « BHLC » de (Murua et al, 2005) est une extension de « Pan » dont le modèle est bayésien hiérarchique avec groupes. Le but principal de ce travail est d'étudier le problème de sélection du modèle pour l'imputation multiple en termes d'efficacité et d'exactitude des prédictions des valeurs manquantes. Nous proposons une mesure de performance liée à la prédiction des valeurs manquantes. La mesure est une erreur quadratique moyenne reflétant la variance associée aux imputations multiples et le biais de prédiction. Nous montrons que cette mesure est plus objective que la mesure de variance de Rubin. Notre mesure est calculée en augmentant par une faible proportion le nombre de valeurs manquantes dans les données. La performance du modèle d'imputation est alors évaluée par l'erreur de prédiction associée aux valeurs manquantes. Pour étudier le problème objectivement, nous avons effectué plusieurs simulations. Les données ont été produites selon des modèles explicites différents avec des hypothèses particulières sur la structure des erreurs et la distribution a priori des valeurs manquantes. Notre étude examine si la vraie structure d'erreur des données a un effet sur la performance du choix des différentes hypothèses formulées pour le modèle d'imputation. Nous avons conclu que la réponse est oui. De plus, le choix de la distribution des valeurs manquantes semble être le facteur le plus important pour l'exactitude des prédictions. En général, les choix les plus efficaces pour de bonnes imputations sont une distribution de student avec inégalité des variances dans les groupes pour la structure des erreurs et une loi a priori choisie pour les valeurs manquantes est la loi normale avec moyenne et variance empirique des données observées, ou celle régularisé avec grande variabilité. Finalement, nous avons appliqué nos idées à un cas réel traitant un problème de santé. Mots clés : valeurs manquantes, imputations multiples, modèle linéaire bayésien hiérarchique, modèle à effets mixtes. / Abstract The technique known as multiple imputation seems to be the most suitable technique for solving the problem of non-response. The literature mentions methods that models the nature and structure of missing values. One of the most popular methods is the PAN algorithm of Schafer and Yucel (2002). The imputations yielded by this method are based on a multivariate linear mixed-effects model for the response variable. A Bayesian hierarchical clustered and more flexible extension of PAN is given by the BHLC model of Murua et al. (2005). The main goal of this work is to study the problem of model selection for multiple imputation in terms of efficiency and accuracy of missing-value predictions. We propose a measure of performance linked to the prediction of missing values. The measure is a mean squared error, and hence in addition to the variance associated to the multiple imputations, it includes a measure of bias in the prediction. We show that this measure is more objective than the most common variance measure of Rubin. Our measure is computed by incrementing by a small proportion the number of missing values in the data and supposing that those values are also missing. The performance of the imputation model is then assessed through the prediction error associated to these pseudo missing values. In order to study the problem objectively, we have devised several simulations. Data were generated according to different explicit models that assumed particular error structures. Several missing-value prior distributions as well as error-term distributions are then hypothesized. Our study investigates if the true error structure of the data has an effect on the performance of the different hypothesized choices for the imputation model. We concluded that the answer is yes. Moreover, the choice of missing-value prior distribution seems to be the most important factor for accuracy of predictions. In general, the most effective choices for good imputations are a t-Student distribution with different cluster variances for the error-term, and a missing-value Normal prior with data-driven mean and variance, or a missing-value regularizing Normal prior with large variance (a ridge-regression-like prior). Finally, we have applied our ideas to a real problem dealing with health outcome observations associated to a large number of countries around the world. Keywords: Missing values, multiple imputation, Bayesian hierarchical linear model, mixed effects model.

Résumé La technique connue comme l'imputation multiple semble être la technique la plus appropriée pour résoudre le problème de non-réponse. La littérature mentionne des méthodes qui modélisent la nature et la structure des valeurs manquantes. Une des méthodes les plus populaires est l'algorithme « Pan » de (Schafer & Yucel, 2002). Les imputations rapportées par cette méthode sont basées sur un modèle linéaire multivarié à effets mixtes pour la variable réponse. La méthode « BHLC » de (Murua et al, 2005) est une extension de « Pan » dont le modèle est bayésien hiérarchique avec groupes. Le but principal de ce travail est d'étudier le problème de sélection du modèle pour l'imputation multiple en termes d'efficacité et d'exactitude des prédictions des valeurs manquantes. Nous proposons une mesure de performance liée à la prédiction des valeurs manquantes. La mesure est une erreur quadratique moyenne reflétant la variance associée aux imputations multiples et le biais de prédiction. Nous montrons que cette mesure est plus objective que la mesure de variance de Rubin. Notre mesure est calculée en augmentant par une faible proportion le nombre de valeurs manquantes dans les données. La performance du modèle d'imputation est alors évaluée par l'erreur de prédiction associée aux valeurs manquantes. Pour étudier le problème objectivement, nous avons effectué plusieurs simulations. Les données ont été produites selon des modèles explicites différents avec des hypothèses particulières sur la structure des erreurs et la distribution a priori des valeurs manquantes. Notre étude examine si la vraie structure d'erreur des données a un effet sur la performance du choix des différentes hypothèses formulées pour le modèle d'imputation. Nous avons conclu que la réponse est oui. De plus, le choix de la distribution des valeurs manquantes semble être le facteur le plus important pour l'exactitude des prédictions. En général, les choix les plus efficaces pour de bonnes imputations sont une distribution de student avec inégalité des variances dans les groupes pour la structure des erreurs et une loi a priori choisie pour les valeurs manquantes est la loi normale avec moyenne et variance empirique des données observées, ou celle régularisé avec grande variabilité. Finalement, nous avons appliqué nos idées à un cas réel traitant un problème de santé. Mots clés : valeurs manquantes, imputations multiples, modèle linéaire bayésien hiérarchique, modèle à effets mixtes. / Abstract The technique known as multiple imputation seems to be the most suitable technique for solving the problem of non-response. The literature mentions methods that models the nature and structure of missing values. One of the most popular methods is the PAN algorithm of Schafer and Yucel (2002). The imputations yielded by this method are based on a multivariate linear mixed-effects model for the response variable. A Bayesian hierarchical clustered and more flexible extension of PAN is given by the BHLC model of Murua et al. (2005). The main goal of this work is to study the problem of model selection for multiple imputation in terms of efficiency and accuracy of missing-value predictions. We propose a measure of performance linked to the prediction of missing values. The measure is a mean squared error, and hence in addition to the variance associated to the multiple imputations, it includes a measure of bias in the prediction. We show that this measure is more objective than the most common variance measure of Rubin. Our measure is computed by incrementing by a small proportion the number of missing values in the data and supposing that those values are also missing. The performance of the imputation model is then assessed through the prediction error associated to these pseudo missing values. In order to study the problem objectively, we have devised several simulations. Data were generated according to different explicit models that assumed particular error structures. Several missing-value prior distributions as well as error-term distributions are then hypothesized. Our study investigates if the true error structure of the data has an effect on the performance of the different hypothesized choices for the imputation model. We concluded that the answer is yes. Moreover, the choice of missing-value prior distribution seems to be the most important factor for accuracy of predictions. In general, the most effective choices for good imputations are a t-Student distribution with different cluster variances for the error-term, and a missing-value Normal prior with data-driven mean and variance, or a missing-value regularizing Normal prior with large variance (a ridge-regression-like prior). Finally, we have applied our ideas to a real problem dealing with health outcome observations associated to a large number of countries around the world. Keywords: Missing values, multiple imputation, Bayesian hierarchical linear model, mixed effects model. / Les logiciels utilisés sont Splus et R.

The main purpose of panel studies is to analyze changes in values of studied variables over time. In micro panel research, a large number of elements are periodically observed within the relatively short time period of just a few years. Moreover, the number of repeated measurements is small. This dissertation deals with contemporary approaches to the regression and the clustering analysis of micro panel data. One of the approaches to the micro panel analysis is to use multivariate statistical models originally designed for crosssectional data and modify them in order to take into account the within-subject correlation. The thesis summarizes available tools for the regression analysis of micro panel data. The known and currently used linear mixed effects models for a normally distributed dependent variable are recapitulated. Besides that, new approaches for analysis of a response variable with other than normal distribution are presented. These approaches include the generalized marginal linear model, the generalized linear mixed effects model and the Bayesian modelling approach. In addition to describing the aforementioned models, the paper also includes a brief overview of their implementation in the R software. The difficulty with the regression models adjusted for micro panel data is the ambiguity of their parameters estimation. This thesis proposes a way to improve the estimations through the cluster analysis. For this reason, the thesis also contains a description of methods of the cluster analysis of micro panel data. Because supply of the methods is limited, the main goal of this paper is to devise its own two-step approach for clustering micro panel data. In the first step, the panel data are transformed into a static form using a set of proposed characteristics of dynamics. These characteristics represent different features of time course of the observed variables. In the second step, the elements are clustered by conventional spatial clustering techniques (agglomerative clustering and the C-means partitioning). The clustering is based on a dissimilarity matrix of the values of clustering variables calculated in the first step. Another goal of this paper is to find out whether the suggested procedure leads to an improvement in quality of the regression models for this type of data. By means of a simulation study, the procedure drafted herein is compared to the procedure applied in the kml package of the R software, as well as to the clustering characteristics proposed by Urso (2004). The simulation study demonstrated better results of the proposed combination of clustering variables as compared to the other combinations currently used. A corresponding script written in the R-language represents another benefit of this paper. It is available on the attached CD and it can be used for analyses of readers own micro panel data.

La résolution des pronoms est le processus par lequel un pronom anaphorique est mis en relation avec son antécédent. Les humains en sont capables sans efforts notables en situation normale. En revanche, les systèmes automatiques ont une performance qui reste loin derrière, malgré des algorithmes de plus en plus sophistiqués, développés par la communauté du Traitement Automatique des Langues. La recherche en psycholinguistique a montré à travers des expériences qu'au cours de la résolution de nombreux facteurs sont pris en compte par les locuteurs. Une question importante se pose : comment les facteurs interagissent et quel poids faut-il attribuer à chacun d'entre eux ? Une deuxième question qui se pose alors est comment les théories linguistiques de la résolution des pronoms incorporent tous les facteurs. Nous proposons une nouvelle approche à ces problématiques : la simulation computationnelle de la charge cognitive de la résolution des pronoms. La motivation pour notre approche est double : d'une part, l'implémentation d'hypothèses par un système computationnel permet de mieux spécifier les théories, d’autre part, les systèmes automatiques peuvent faire des prédictions sur des données naturelles comme les corpus de mouvement oculaires. De cette façon, les modèles computationnels représentent une alternative aux expériences classiques avec des items expérimentaux construits manuellement. Nous avons fait plusieurs expériences afin d'explorer les modèles cognitifs computationnels de la résolution des pronoms. D'abord, nous avons simulé la charge cognitive des pronoms en utilisant des poids de facteurs de résolution appris sur corpus. Ensuite, nous avons testé si les concepts de la Théorie de l’Information sont pertinents pour prédire la charge cognitive des pronoms. Finalement, nous avons procédé à l’évaluation d’un modèle psycholinguistique sur des données issues d’un corpus enrichi de mouvements oculaires. Les résultats de nos expériences montrent que la résolution des pronoms est en effet multi-factorielle et que l’influence des facteurs peut être estimée sur corpus. Nos résultats montrent aussi que des concepts de la Théorie de l’Information sont pertinents pour la modélisation des pronoms. Nous concluons que l’évaluation des théories sur des données de corpus peut jouer un rôle important dans le développement de ces théories et ainsi amener dans le futur à une meilleure prise en compte du contexte discursif. / Pronoun resolution is the process in which an anaphoric pronoun is linked to its antecedent. In a normal situation, humans do not experience much cognitive effort due to this process. However, automatic systems perform far from human accuracy, despite the efforts made by the Natural Language Processing community. Experimental research in the field of psycholinguistics has shown that during pronoun resolution many linguistic factors are taken into account by speakers. An important question is thus how much influence each of these factors has and how the factors interact with each-other. A second question is how linguistic theories about pronoun resolution can incorporate all relevant factors. In this thesis, we propose a new approach to answer these questions: computational simulation of the cognitive load of pronoun resolution. The motivation for this approach is two-fold. On the one hand, implementing hypotheses about pronoun resolution in a computational system leads to a more precise formulation of theories. On the other hand, robust computational systems can be run on uncontrolled data such as eye movement corpora and thus provide an alternative to hand-constructed experimental material. In this thesis, we conducted various experiments. First, we simulated the cognitive load of pronouns by learning the magnitude of impact of various factors on corpus data. Second, we tested whether concepts from Information Theory were relevant to predict the cognitive load of pronoun resolution. Finally, we evaluated a theoretical model of pronoun resolution on a corpus enriched with eye movement data. Our research shows that multiple factors play a role in pronoun resolution and that their influence can be estimated on corpus data. We also demonstrate that the concepts of Information Theory play a role in pronoun resolution. We conclude that the evaluation of hypotheses on corpus data enriched with cognitive data ---- such as eye movement data --- play an important role in the development and evaluation of theories. We expect that corpus based methods will lead to a better modelling of the influence of discourse structure on pronoun resolution in future work.

This thesis employs the globalization and integration-demarcation cleavage theory formulated by Huttar [2014] and Kriesi [2012], conception of populism formulated by Mudde [2017] and draws on Gramscian conception of civil society and hegemony. Aim of this thesis is to build a model of causal influence of globalization on cleavage and on populism, as was suggested by Hutter [2014]. After building this model, the aim is to explore how this theoretical relationship hold's over the 30 years since 90's, when the connection between globalization and new sociocultural cleavage had been theoretically suggested. For this model I am using KOF Globalization Index, European Values Survey datasets and Authoritarian Populism Index constructed and published by Timbro in years 1990, 1999, 2008 and 2017. This model is built on a dataset containing 38 countries on European continent or being a candidate country for EU. I am elaborating Hutter's theoretical suggestion and framing it in Gramscian conception of civil society. This allows me to suggest that populists are using organic crisis in a society to attract people who feel disjointed from current hegemonical elite and to create counterhegemony. The theory is, that globalization increases the tension between winners and losers of globalization sides of cleavage...