Made available in DSpace on 2016-06-02T20:04:53Z (GMT). No. of bitstreams: 1 6714.pdf: 1130315 bytes, checksum: 4ce881df9c6c0f6451cae6908855d277 (MD5) Previous issue date: 2015-01-14 / Financiadora de Estudos e Projetos / We present a class of nonlinear truncated mixed-effects models where the truncation nature of the data is incorporated into the statistical model by assuming that the variable of interest, namely the truncated variable, follows a truncated distribution which, in turn, corresponds to a conditional distribution obtained by restricting the support of a given probability distribution function. The family of nonlinear truncated mixed-effects models for location and scale is constructed based on the perspective of nonlinear generalized mixed-effects models and by assuming that the distribution of response variable belongs to a truncated class of distributions indexed by a location and a scale parameter. The location parameter of the response variable is assumed to be associated with a continuous nonlinear function of covariates and unknown parameters and with unobserved random effects, and the scale parameter of the responses is assumed to be characterized by a continuous function of the covariates and unknown parameters. The proposed truncated nonlinear mixed-effects models are constructed assuming both random truncation limits; however, truncated nonlinear mixed-effects models with fixed known limits are readily obtained as particular cases of these models. For models constructed under the assumption of random truncation limits, the likelihood function of the observed data shall be a function both of the parameters of the truncated distribution of the truncated variable and of the parameters of the distribution of the truncation variables. For the particular case of fixed known truncation limits, the likelihood function of the observed data is a function only of the parameters of the truncated distribution assumed for the variable of interest. The likelihood equation resulting from the proposed truncated nonlinear regression models do not have analytical solutions and thus, under the frequentist inferential perspective, the model parameters are estimated by direct maximization of the log-likelihood using an iterative procedure. We also consider diagnostic analysis to check for model misspecification, outliers and influential observations using standardized residuals, and global and local influence metrics. Under the Bayesian perspective of statistical inference, parameter estimates are computed based on draws from the posterior distribution of parameters obtained using an Markov Chain Monte Carlo procedure. Posterior predictive checks, Bayesian standardized residuals and a Bayesian influence measures are considered to check for model adequacy, outliers and influential observations. As Bayesian model selection criteria, we consider the sum of log -CPO and a Bayesian model selection procedure using a Bayesian mixture model framework. To illustrate the proposed methodology, we analyze soil-water retention, which are used to construct soil-water characteristic curves and which are subject to truncation since soil-water content (the proportion of water in soil samples) is limited by the residual soil-water content and the saturated soil-water content. / Neste trabalho, apresentamos uma classe de modelos não lineares truncados mistos onde a característica de truncamento dos dados é incorporada ao modelo estatístico assumindo-se que a variável de interesse, isto é, a variável truncada, possui uma função de distribuição truncada que, por sua vez, corresponde a uma função de distribuição condicional obtida ao se restringir o suporte de alguma função de distribuição de probabilidade. A família de modelos não lineares truncados mistos para locação e escala é construída sob a perspectiva de modelos não lineares generalizados mistos e considerando uma classe de distribuições indexadas por parâmetros de locação e escala. Assumimos que o parâmetro de locação da variável resposta é associado a uma função não linear contínua de um conjunto de covariáveis e parâmetros desconhecidos e a efeitos aleatórios não observáveis, e que o parâmetro de escala das respostas pode ser caracterizado por uma função contínua das covariáveis e de parâmetros desconhecidos. Os modelos não lineares truncados mistos para locação e escala, aqui apresentados, são construídos supondo limites de truncamento aleatórios, porém, modelos não lineares truncados mistos com limites fixos e conhecidos são prontamente obtidos como casos particulares desses modelos. Nos modelos construídos sob a suposição de limites de truncamentos aleatórios, a função de verossimilhança é escrita em função dos parâmetros da distribuição da variável resposta truncada e dos parâmetros das distribuições das variáveis de truncamento. Para o caso particular de limites fixos e conhecidos, a função de verossimilhança será apenas uma função dos parâmetros da distribuição truncada assumida para a variável resposta de interesse. As equações de verossimilhança dos modelos, aqui propostos, não possuem soluções analíticas e, sob a perspectiva frequentista de inferência estatística, os parâmetros do modelo são estimados pela maximização direta da função de log-verossimilhança via um procedimento iterativo. Consideramos, também, uma análise de diagnóstico para verificar a adequação do modelo, observações discrepantes e/ou influentes, usando resíduos padronizados e medidas de influência global e influência local. Sob a perspectiva Bayesiana de inferência estatística, as estimativas dos parâmetros dos modelos propostos são definidas como as médias a posteriori de amostras obtidas via um algoritmo do tipo cadeia de Markov Monte Carlo das distribuições a posteriori dos parâmetros. Para a análise de diagnóstico Bayesiano do modelo, consideramos métricas de avaliação preditiva a posteriori, resíduos Bayesianos padronizados e a calibração de casos para diagnóstico de influência. Como critérios Bayesianos de seleção de modelos, consideramos a soma de log -CPO e um critério de seleção de modelos baseada na abordagem Bayesiana de mistura de modelos. Para ilustrar a metodologia proposta, analisamos dados de retenção de água em solo, que são usados para construir curvas de retenção de água em solo e que estão sujeitos a truncamento pois as medições de umidade de água (a proporção de água presente em amostras de solos) são limitadas pela umidade residual e pela umidade saturada do solo amostrado.

Consider life testing of J-component series systems that are subjected to stress levels that are steeper than that at normal usage condition. The objective of performing such life tests, commonly known as Accelerated Life Testing (ALT) in the literature, is to collect observations on system failure times within a limited time frame. The accelerated observations are then used to infer on the component and system reliability metrics at usage stress. In this thesis, the existing literature is first extended by considering the general case of K stress variables, as opposed to the usual consideration of a single stress variable. Next, a general model assuming that the component log-lifetimes belong to an arbitrary location-scale family of distributions, is formulated. The location parameters are assumed to depend on the stress variables through a general stress translation function, while the scale parameters are assumed to be independent of the stress variables. This formulation covers the standard lifetime distributions as well as well-known stress translation functions as special cases. Bayesian methodologies are then developed for four special cases of the proposed general model, viz., exponentials, Weibulls with equal shape parameter, Weibulls with distinct shape parameters and log-normals with distinct scale parameters. For exponential and Weibull models, the priors on lifetime parameters are assumed to be log-concave and independent of each other. The resulting univariate conditional posterior of each lifetime parameter given the rest, is shown to be log-concave. This facilitates Gibbs sampling from the joint posterior of lifetime parameters. Propriety of the joint posteriors with Laplacian uniform priors on stress coefficients are also proved under a suitable set of sufficient conditions. For the log-normal model, the observed data is first augmented with log-lifetimes of un-failed components to form complete data. A Gibbs sampling scheme is then developed to generate observations from the joint posterior of lifetime parameters, through the augmented data and a conjugate prior for the complete data. In all four cases, Bayesian predictive inference techniques are used to study component and system reliability metrics at usage stress. Though this thesis mainly deals with Bayesian inference of accelerated data of series systems, maximum likelihood analysis for the log-normal component lifetimes is also performed via an expectation-maximization (EM) algorithm and bootstrap, which are not available in the literature. The last part of this thesis deals with construction of optimal Bayesian designs for accelerated life tests of J-component series systems under Type-I censoring scheme. Optimal ALT plans for a single stress variable are obtained using two different Bayesian D-optimality criteria for exponentially distributed component lives. A detailed sensitivity analysis is carried out to investigate the effect of different planning inputs on the optimal designs as well.

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.

Für Entwurf, Modellierung sowie Überwachung von Gasphasenprozessen sind fun-dierte Kenntnisse über elementare Zustandsgrößen wie Temperatur oder Spezieskon-zentration unerlässlich. Obwohl bereits heute eine breite Palette an optischen, nicht-invasiven Online-Messtechniken zu Verfügung steht, ist deren Einsatz noch immer auf wenige Anwendungsfelder beschränkt. Die Gründe dafür liegen im oft hohen ex-perimentellen Aufwand oder in anderen Nachteilen wie der Notwendigkeit zum Einsatz von Tracern oder der Kalibrierung über zusätzliche Referenzen. Um diese Nachteile zu umgehen, wurde im Rahmen dieser Arbeit ein mobiles, faserbasiertes Sensorsystem, basierend auf der spontanen Raman-Spektroskopie entwickelt. Die Technik verwendet durchstimmbare NIR-Dauerstrich-Laser-Anregung, Signalerfassung in rückstreuender Geometrie (Punktmessung) und erfordert weder Probennahme, noch Tracer innerhalb der Strömung oder Kalibrierschritte am zu untersuchenden Prozess. Die Methode ermöglicht die simultane Bestimmung von Gastemperaturen und Spezieskonzentrationen sowie im Falle von Aerosolen die Bestimmung der Partikelspezies und der Anteile ihrer polymorphen Kristallstrukturen. Die Datenauswertung basiert auf der Rekonstruktion der gemessenen Spektren anhand simulierter Modellspektren durch Least-Square-Algorithmen. Herkömmliche Ansätze liefern lediglich Parameter, die das Residuum zwischen Simulation und Messsignal minimieren. Unsicherheiten der Messgrößen sind daraus nicht ermittelbar und werden deshalb konventionell durch Wiederholung der Messung bestimmt. Mit Hilfe der hier eingesetzten Bayes'schen Statistik lassen sich die entsprechenden Unsicherheiten direkt bestimmen. Darüber hinaus ermöglicht der Ansatz das Einbeziehen von Vorwissen zur Verbesserung der Robustheit und Genauigkeit der Auswertung. Die Performance des Sensorsystems wurde durch Einsätze an verschiedenen Gasphasenprozessen getestet und evaluiert. Dazu gehören Test-Aerosole, ein TiO2-Nanopartikelsyntheseprozess sowie eine laminare, rußarme Flamme. Ein leicht modifiziertes Sensorsystem (VIS-Anregung) wurde an einem Vergasungsreaktor eingesetzt. Generell konnte eine hohe Qualität der ermittelten Messgrößen festgestellt werden. So sind deren Unsicherheiten mit denen deutlich komplexerer Messtechniken vergleichbar, stellenweise sogar geringer. Die mittlere Unsicherheit der Gastemperaturen innerhalb der Flamme betrug nur 1,6 %. Somit ermöglicht der vorgestellte Sensor bei geringem experimentellen Aufwand die Bestimmung wertvoller Prozessdaten und stellt so potentiell die Basis für eine breitere Anwendung optischer Prozessmesstechnik dar. / For the design, modelling and monitoring of gas-phase processes a profound knowledge of elementary state variables such as temperature or species concentration is essential. Although a wide range of optical, non-invasive online measurement techniques is already available today, their use is still limited to a few fields of application. The reasons for this are the regularly high experimental effort or other disadvantages such as the necessity to use tracers or to execute calibration via additional references. In order to avoid these disadvantages, a mobile, fiber-based sensor system based on spontaneous Raman spectroscopy was developed within the scope of this work. The technique uses tunable NIR continuous-wave laser excitation, signal acquisition in backscattering geometry (point measurement) and requires neither sampling, tracers within the flow nor calibration steps at the process under investigation. The method allows the simultaneous determination of gas temperatures and species concentrations and, in the case of aerosols, the determination of the particle species and their polymorphic crystal structures. The data evaluation is based on the reconstruction of the measured spectra using simulated model spectra through least square algorithms. Conventional approaches only provide parameters that minimize the residual between simulation and measurement signal. Uncertainties of the measured variables cannot be determined from these parameters and are, therefore, determined conventionally by repeating the measurement. With the help of the Bayesian statistics used here, the corresponding uncertainties can be determined directly. Furthermore, the approach allows the inclusion of prior knowledge to improve the robustness and accuracy of the evaluation. The performance of the sensor system was tested and evaluated by using it in different gas phase processes. These include test aerosols, a TiO2 nanoparticle synthesis process and a laminar weakly sooting flame. A slightly modified system (VIS excitation) was used with a similar operation strategy at a gasification reactor. In general, a high quality of the measured variables could be determined. Their uncertainties are comparable with those of much more complex measuring techniques, in some cases even lower. The mean uncertainty of the gas temperatures within the flame was only 1.6 %. Thus, the presented sensor enables the determination of valuable process data with low experimental effort and can potentially be the basis for a broader application of optical process measurement technology.

La modélisation par équations structurelles est très répandue dans des domaines très variés et nous l'appliquons pour la première fois en métrologie dans le traitement de données de comparaisons interlaboratoires. Les modèles à équations structurelles à variables latentes sont des modèles multivariés utilisés pour modéliser des relations de causalité entre des variables observées (les données). Le modèle s'applique dans le cas où les données peuvent être regroupées dans des blocs disjoints où chaque bloc définit un concept modélisé par une variable latente. La structure de corrélation des variables observées est ainsi résumée dans la structure de corrélation des variables latentes. Nous proposons une approche bayésienne des modèles à équations structurelles centrée sur l'analyse de la matrice de corrélation des variables latentes. Nous appliquons une expansion paramétrique à la matrice de corrélation des variables latentes afin de surmonter l'indétermination de l'échelle des variables latentes et d'améliorer la convergence de l'algorithme de Gibbs utilisé. La puissance de l'approche structurelle nous permet de proposer une modélisation riche et flexible des biais de mesure qui vient enrichir le calcul de la valeur de consensus et de son incertitude associée dans un cadre entièrement bayésien. Sous certaines hypothèses l'approche permet de manière innovante de calculer les contributions des variables de biais au biais des laboratoires. Plus généralement nous proposons un cadre bayésien pour l'amélioration de la qualité des mesures. Nous illustrons et montrons l'intérêt d'une modélisation structurelle des biais de mesure sur des comparaisons interlaboratoires en environnement. / Structural equation modelling is a widespread approach in a variety of domains and is first applied here to interlaboratory comparisons in metrology. Structural Equation Models with latent variables (SEM) are multivariate models used to model causality relationships in observed variables (the data). It is assumed that data can be grouped into separate blocks each describing a latent concept modelled by a latent variable. The correlation structure of the observed variables is transferred into the correlation structure of the latent variables. A Bayesian approach of SEM is proposed based on the analysis of the correlation matrix of latent variables using parameter expansion to overcome identifiability issues and improving the convergence of the Gibbs sampler. SEM is used as a powerful and flexible tool to model measurement bias with the aim of improving the reliability of the consensus value and its associated uncertainty in a fully Bayesian framework. The approach also allows to compute the contributions of the observed variables to the bias of the laboratories, under additional hypotheses. More generally a global Bayesian framework is proposed to improve the quality of measurements. The approach is illustrated on the structural equation modelling of measurement bias in interlaboratory comparisons in environment.