Semiparametric modeling is a hybrid of the parametric and nonparametric modelings where some function forms are known and others are unknown. In this dissertation, we have made several contributions to semiparametric modeling based on the single index model related to the following three topics: the first is to propose a model for detecting change points simultaneously with estimating the unknown function; the second is to develop two models for spatially correlated data; and the third is to further develop two models for spatially-temporally correlated data. To address the first topic, we propose a unified approach in its ability to simultaneously estimate the nonlinear relationship and change points. We propose a single index change point model as our unified approach by adjusting for several other covariates. We nonparametrically estimate the unknown function using kernel smoothing and also provide a permutation based testing procedure to detect multiple change points. We show the asymptotic properties of the permutation testing based procedure. The advantage of our approach is demonstrated using the mortality data of Seoul, Korea from January, 2000 to December, 2007. On the second topic, we propose two semiparametric single index models for spatially correlated data. One additively separates the nonparametric function and spatially correlated random effects, while the other does not separate the nonparametric function and spatially correlated random effects. We estimate these two models using two algorithms based on Markov Chain Expectation Maximization algorithm. Our approaches are compared using simulations, suggesting that the semiparametric single index nonadditive model provides more accurate estimates of spatial correlation. The advantage of our approach is demonstrated using the mortality data of six cities, Korea from January, 2000 to December, 2007. The third topic involves proposing two semiparametric single index models for spatially and temporally correlated data. Our first model has the nonparametric function which can separate from spatially and temporally correlated random effects. We refer it to "semiparametric spatio-temporal separable single index model (SSTS-SIM)", while the second model does not separate the nonparametric function from spatially correlated random effects but separates the time random effects. We refer our second model to "semiparametric nonseparable single index model (SSTN-SIM)". Two algorithms based on Markov Chain Expectation Maximization algorithm are introduced to simultaneously estimate parameters, spatial effects, and times effects. The proposed models are then applied to the mortality data of six major cities in Korea. Our results suggest that SSTN-SIM is more flexible than SSTS-SIM because it can estimate various nonparametric functions while SSTS-SIM enforces the similar nonparametric curves. SSTN-SIM also provides better estimation and prediction. / Ph. D.

Yes / During flooding, the suspended sediment transport usually experiences a wide-range of dilute to hyper-concentrated suspended sediment transport depending on the local flow and ground con-ditions. This paper assesses the distribution of sediment for a variety of hyper-concentrated and dilute flows. Due to the differences between hyper-concentrated and dilute flows, a linear-power coupled model is proposed to integrate these considerations. A parameterised method combining the sediment size, Rouse number, mean concentration, and flow depth parameters has been used for modelling the sediment profile. The accuracy of the proposed model has been verified against the reported laboratory measurements and comparison with other published analytical methods. The proposed method has been shown to effectively compute the concentration profile for a wide range of suspended sediment conditions from hyper-concentrated to dilute flows. Detailed com-parisons reveal that the proposed model calculates the dilute profile with good correspondence to the measured data and other modelling results from literature. For the hyper-concentrated profile, a clear division of lower (bed-load) to upper layer (suspended-load) transport can be observed in the measured data. Using the proposed model, the transitional point from this lower to upper layer transport can be calculated precisely.

Insurance is built on the principle that a group of people contributes to a common pool of money which will be used to cover the costs for individuals who suffer from the insured event. In a competitive market, an insurance company will only be profitable if their pricing reflects the covered risks as good as possible. This thesis investigates the recently proposed Combined Actuarial Neural Network (CANN), a model nesting the traditional Generalised Linear Model (GLM) used in insurance pricing into a Neural Network (NN). The main idea of utilising NNs for insurance pricing is to model interactions between features that the GLM is unable to capture. The CANN model is analysed in a commercial insurance setting with respect to two research questions. The first research question, RQ 1, seeks to answer if the CANN model can outperform the underlying GLM with respect to error metrics and actuarial model evaluation tools. The second research question, RQ 2, seeks to identify existing interpretability methods that can be applied to the CANN model and also showcase how they can be applied. The results for RQ 1 show that CANN models are able to consistently outperform the GLM with respect to chosen model evaluation tools. A literature search is conducted to answer RQ 2, identifying interpretability methods that either are applicable or are possibly applicable to the CANN model. One interpretability method is also proposed in this thesis specifically for the CANN model, using model-fitted averages on two-dimensional segments of the data. Three interpretability methods from the literature search and the one proposed in this thesis are demonstrated, illustrating how these may be applied. / Försäkringar bygger på principen att en grupp människor bidrar till en gemensam summa pengar som används för att täcka kostnader för individer som råkar ut för den försäkrade händelsen. I en konkurrensutsatt marknad kommer försäkringsbolag endast vara lönsamma om deras prissättning är så bra som möjligt. Denna uppsats undersöker den nyligen föreslagna Combined Actuarial Neural Network (CANN) modellen som bygger in en Generalised Linear Model (GLM) i ett neuralt nätverk, i en praktiskt och kommersiell försäkringskontext med avseende på två forskningsfrågor. Huvudidén för en CANN modell är att fånga interaktioner mellan variabler, vilket en GLM inte automatiskt kan göra. Forskningsfråga 1 ämnar undersöka huruvida en CANN modell kan prestera bättre än en GLM med avseende på utvalda statistiska prestationsmått och modellutvärderingsverktyg som används av aktuarier. Forskningsfråga 2 ämnar identifiera några tolkningsverktyg som kan appliceras på CANN modellen samt demonstrera hur de kan användas. Resultaten för Forskningsfråga 1 visar att CANN modellen kan prestera bättre än en GLM. En literatursökning genomförs för att svara på Forskningsfråga 2, och ett antal tolkningsverktyg identifieras. Ett tolkningsverktyg föreslås också i denna uppsats specifikt för att tolka CANN modellen. Tre av tolkningsverktygen samt det utvecklade verktyget demonstreras för att visa hur de kan användas för att tolka CANN modellen.

Insurance is built on the principle that a group of people contributes to a common pool of money which will be used to cover the costs for individuals who suffer from the insured event. In a competitive market, an insurance company will only be profitable if their pricing reflects the covered risks as good as possible. This thesis investigates the recently proposed Combined Actuarial Neural Network (CANN), a model nesting the traditional Generalised Linear Model (GLM) used in insurance pricing into a Neural Network (NN). The main idea of utilising NNs for insurance pricing is to model interactions between features that the GLM is unable to capture. The CANN model is analysed in a commercial insurance setting with respect to two research questions. The first research question, RQ 1, seeks to answer if the CANN model can outperform the underlying GLM with respect to error metrics and actuarial model evaluation tools. The second research question, RQ 2, seeks to identify existing interpretability methods that can be applied to the CANN model and also showcase how they can be applied. The results for RQ 1 show that CANN models are able to consistently outperform the GLM with respect to chosen model evaluation tools. A literature search is conducted to answer RQ 2, identifying interpretability methods that either are applicable or are possibly applicable to the CANN model. One interpretability method is also proposed in this thesis specifically for the CANN model, using model-fitted averages on two-dimensional segments of the data. Three interpretability methods from the literature search and the one proposed in this thesis are demonstrated, illustrating how these may be applied. / Försäkringar bygger på principen att en grupp människor bidrar till en gemensam summa pengar som används för att täcka kostnader för individer som råkar ut för den försäkrade händelsen. I en konkurrensutsatt marknad kommer försäkringsbolag endast vara lönsamma om deras prissättning är så bra som möjligt. Denna uppsats undersöker den nyligen föreslagna Combined Actuarial Neural Network (CANN) modellen som bygger in en Generalised Linear Model (GLM) i ett neuralt nätverk, i en praktiskt och kommersiell försäkringskontext med avseende på två forskningsfrågor. Huvudidén för en CANN modell är att fånga interaktioner mellan variabler, vilket en GLM inte automatiskt kan göra. Forskningsfråga 1 ämnar undersöka huruvida en CANN modell kan prestera bättre än en GLM med avseende på utvalda statistiska prestationsmått och modellutvärderingsverktyg som används av aktuarier. Forskningsfråga 2 ämnar identifiera några tolkningsverktyg som kan appliceras på CANN modellen samt demonstrera hur de kan användas. Resultaten för Forskningsfråga 1 visar att CANN modellen kan prestera bättre än en GLM. En literatursökning genomförs för att svara på Forskningsfråga 2, och ett antal tolkningsverktyg identifieras. Ett tolkningsverktyg föreslås också i denna uppsats specifikt för att tolka CANN modellen. Tre av tolkningsverktygen samt det utvecklade verktyget demonstreras för att visa hur de kan användas för att tolka CANN modellen.

The developments of advanced non-linear control strategies have attracted a considerable research interests over the past decades especially in process control. Rather than an absolute reliance on mathematical models of process plants which often brings discrepancies especially owing to design errors and equipment degradation, non-linear models are however required because they provide improved prediction capabilities but they are very difficult to derive. In addition, the derivation of the global optimal solution gets more difficult especially when multivariable and non-linear systems are involved. Hence, this research investigates soft computing techniques for the implementation of a novel real time constrained non-linear model predictive controller (NMPC). The time-frequency localisation characteristics of wavelet neural network (WNN) were utilised for the non-linear models design using system identification approach from experimental data and improve upon the conventional artificial neural network (ANN) which is prone to low convergence rate and the difficulties in locating the global minimum point during training process. Salient features of particle swarm optimisation and a genetic algorithm (GA) were combined to optimise the network weights. Real time optimisation occurring at every sampling instant is achieved using a GA to deliver results both in simulations and real time implementation on coupled tank systems with further extension to a complex quadruple tank process in simulations. The results show the superiority of the novel WNN-NMPC approach in terms of the average controller energy and mean squared error over the conventional ANN-NMPC strategies and PID control strategy for both SISO and MIMO systems.

A recent development in the design of control system for a jet engine is to use a suitable, fast and accurate model running on board. Development of linear models is particularly important as most engine control designs are based on linear control theory. Engine control performance can be significantly improved by increasing the accuracy of the developed model. Current state-of-the-art is to use piecewise linear models at selected equilibrium conditions for the development of set point controllers, followed by scheduling of resulting controller gains as a function of one or more of the system states. However, arriving at an effective gain scheduler that can accommodate fast transients covering a wide range of operating points can become quite complex and involved, thus resulting in a sacrifice on controller performance for its simplicity. This thesis presents a methodology for developing a control oriented analytical linear model of a jet engine at both equilibrium and off-equilibrium conditions. This scheme requires a nonlinear engine model to run onboard in real time. The off-equilibrium analytical linear model provides improved accuracy and flexibility over the commonly used piecewise linear models developed using numerical perturbations. Linear coefficients are obtained by evaluating, at current conditions, analytical expressions which result from differentiation of simplified nonlinear expressions. Residualization of the fast dynamics states are utilized since the fast dynamics are typically outside of the primary control bandwidth. Analytical expressions based on the physics of the aerothermodynamic processes of a gas turbine engine facilitate a systematic approach to the analysis and synthesis of model based controllers. In addition, the use of analytical expressions reduces the computational effort, enabling linearization in real time at both equilibrium and off-equilibrium conditions for a more accurate capture of system dynamics during aggressive transient maneuvers. The methodology is formulated and applied to a separate flow twin-spool turbofan engine model in the Numerical Propulsion System Simulation (NPSS) platform. The fidelity of linear model is examined by validating against a detailed nonlinear engine model using time domain response, the normalized additive uncertainty and the nu-gap metric. The effects of each simplifying assumptions, which are crucial to the linear model development, on the fidelity of the linear model are analyzed in detail. A case study is performed to investigate the case when the current state (including both slow and fast states) of the system is not readily available from the nonlinear simulation model. Also, a simple model based control is used to illustrate benefits of using the proposed modeling approach.

本論文從教育社會學角度探討造成數學成就性別差異現象的成因，以班級的性別環境為研究脈絡，研究影響國中女生數學成就的可能原因。假設數學成就的性別差異是受到後天學習歷程影響，班級環境中隱含的性別刻板印象為其中一個重要社會文化影響因素。透過比較國一到國三階段女生班和一般男女合班女生數學成就的異同，嘗試找出造成數學成就性別差異現象的成因，是否與班級性別環境、師生的性別刻板印象等因素有關。利用階層線性模式（Hierarchical Linear Models，HLM）統計方法，分析資料取自由中央研究院、教育部和國科會共同規劃的全國性長期的調查計畫：「台灣教育長期追蹤資料庫」（Taiwan Education Panel Survey，簡稱TEPS）。研究結果發現女生班、數學老師性別及班級學業氣氛等因素對於國中女生數學成就有顯著影響力，但進一步考慮學校公私別變項之後，女生班的影響力即消失。 / The main purpose of this study is to assess the magnitude of individual and contextual influences to explain gender differences in math achievements. Adopting the hierarchical linear model analysis to determine whether or not statistically significant differences between the mathematical achievements of 7th grade students who attend all-girls classes compared with those who attend coeducational classes at the same time, and their academic performance after two years. The result shows that there are three factors that have significant influences on girls’ math achievement in junior high schools, which are the single-sex classes, female math teachers and the academic climate of each class. However, if private schools are taken into consideration, the significant influence of the gender composition of classes will disappear.

多年來，交通運輸與土地使用之交互影響關係受學界所廣泛討論，本研究主要探討高速鐵路與土地使用之交互影響關係。關於高鐵對土地使用影響之研究，分為兩大類別，分別為建立模式預測未來地區發展狀況，以及實證分析高鐵通車後對地區的影響效果。過去研究指出，高鐵營運後，可能對土地使用產生之影響包括：無顯著之土地使用改變、地區間互動改變、聚集效果（Cluster effect）、離散效果(Disparties)以及「隧道效果(Tunnel effect)」或「廊道效果(Corridor effect) 」。 　　本研究為以階層線性模型分析高鐵通車後對台灣土地使用影響之實證研究。根據實證，高鐵站之有無以及高鐵站所在區位對鄉鎮市區土地使用有顯著影響，且相較其他控制變數，為影響鄉鎮市區土地使用之重要變數。有高鐵站之鄉鎮市區與無高鐵站之鄉鎮市區相比，土地使用可能成長較多，而位於高鐵一定服務範圍內之鄉鎮市區之土地使用，亦受高鐵所影響。另外，不同區位之高鐵站對土地使用之效果有所不同，而該區位效果隨產業特性可能有所差異。人口、及業人口以及三級產業及業人口可能因市中心區位之高鐵站聚集，但二級產業及業人口未有因市中心區位高鐵站而聚集的現象；郊區區位之高鐵站鄉鎮市區或縣市，則有人口、及業人口或三級產業及業人口流失的現象。由上述結果可驗證，高鐵服務範圍內有聚集效果之發生，而不同區位之高鐵站，聚集之效果並不同。 / For many years, the interactive relationship between transportation and land use has been widely discussed by scholars. This study is trying to assess the short-term impact of high-speed rail (HSR) on land use. There are two types of studies on the impact of high-speed rail on land use. One is establishing models to predict future land use development; the other is evaluating the effect of HSR empirically. Past studies have shown that possible impacts on land use after the operation of HSR include: no significant land use change, inter-regional interaction change, cluster effect, disparities, and "tunnel effect" or "corridor effect." 　　In this empirical study, the results of hierarchical linear model show that the existence of the HSR station and the location of the HSR station have a significant effect on the land use in the city. Controlling for other control variables, the existence and location of the HSR station are important factors influencing the land use in the city. Land use development in cities with the HSR station may be more evident than those without the HSR station. Cities within the HSR service area are also effected by HSR. In addition, there may be different land use effects due to different locations of the HSR stations, and these location effects may be different due to different industrial characteristics of the area. Population, employment, and employment of tertiary industrial sectors in a city may cluster due to the HSR station in central area location, but employment of secondary industrial sectors doesn’t. Otherwise, population, employment, and employment of tertiary industrial sectors in a city or county may lose due to the HSR station in rural area location. In conclusion, there is a cluster effect within the HSR service area, and this effect varies according to the location of the HSR station.

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.

La scoliose idiopathique de l’adolescent est une déformation 3D du rachis. La littérature comporte une multitude d’études sur la prédiction de l’évolution et l’identification de facteurs de risque de progression. Pour l’instant les facteurs de risque établis sont l’amplitude de la déformation, la maturité squelettique et le type de courbure. Plusieurs autres champs ont été explorés comme les aspects génétiques, biochimiques, mécaniques, posturaux et topographiques, sans vraiment apporter beaucoup de précision à la prédiction de l’évolution. L’avancement de la technologie permet maintenant de générer des reconstructions 3D du rachis à l’aide des radiographies standard et d’obtenir des mesures de paramètres 3D. L’intégration de ces paramètres 3D dans un modèle prédictif représente une avenue encore inexplorée qui est tout à fait logique dans le contexte de cette déformation 3D du rachis. L’objectif général de cette thèse est de développer un modèle de prédiction de l’angle de Cobb à maturité squelettique à partir de l’information disponible au moment de la première visite, soit l’angle de Cobb initial, le type de courbure, l’âge osseux et des paramètres 3D du rachis. Dans une première étude, un indice d’âge osseux a été développé basé sur l’ossification de l’apophyse iliaque et sur le statut du cartilage triradié. Cet indice comporte 3 stades et le second stade, qui est défini par un cartilage triradié fermé avec maximum 1/3 d’ossification de l’apophyse iliaque, représente le moment pendant lequel la progression de la scoliose idiopathique de l’adolescent est la plus rapide. Une seconde étude rétrospective a permis de mettre en évidence le potentiel des paramètres 3D pour améliorer la prédiction de l’évolution. Il a été démontré qu’à la première visite il existe des différences pour 5 paramètres 3D du rachis entre un groupe de patients qui sera éventuellement opéré et un groupe qui ne progressera pas. Ces paramètres sont : la moyenne da la cunéiformisation 3D des disques apicaux, la rotation intervertébrale à la jonction inférieure de la courbure, la torsion, le ratio hauteur/largeur du corps vertébral de T6 et de la colonne complète. Les deux dernières études sont basées sur une cohorte prospective de 133 patients avec une scoliose idiopathique de l’adolescent suivi dès leur première visite à l’hôpital jusqu’à maturité squelettique. Une première étude a permis de mettre en évidence les différences morphologiques à la première visite entre les patients ayant progresser de plus ou moins de 6°. Des différences ont été mise en évidence pour la cyphose, l’angle de plan de déformation maximal, la rotation ntervertébrale l’apex, la torsion et plusieurs paramètres de «slenderness». Ensuite une seconde étude a permis de développer un modèle prédictif basé sur un modèle linéaire général en incluant l’indice d’âge osseux développé dans la première étude, le type de courbure, l’amplitude de l’angle de Cobb à la première visite, l’angle de déformation du plan maximale, la cunéiformisation 3D des disques T3-T4, T8-­T9, T11-­T12 et la somme des cunéiformisation 3D de tous les disques thoraciques et lombaires. Le coefficient de détermination multiple pour cette modélisation est de 0.715. Le modèle prédictif développé renforce l’importance de considérer la scoliose idiopathique dans les trois dimensions et il permettra d’optimiser la prédiction de l’évolution au moment de la première visite. / Prediction of curve progression remains a challenge for the clinicians at the first visit for a patient with adolescent idiopathic scoliosis. Prediction of progression is based on curve type, curve magnitude and skeletal or chronological age. The failure to accurately predict the risk of progression can lead to inadequate treatment, as well as unnecessary medical visits and radiographs. Three-­dimensional evaluation is currently more popular in the scoliosis research community either for classification or treatment planning. The global objective of this thesis was to develop a predictive model of the final Cobb angle in adolescent idiopathic scoliosis based on 3D spine parameters and on skeletal age, curve type and curve magnitude. The first study was to develop a skeletal maturity system based on ossification of iliac apophysis and triradiate cartilage status, two details available on routine radiographs. A 3 stages system was develop with the second stage being associated to the rapid acceleration phase of the deformation. The second stage corresponds to a closed triradiate cartilage and a maximum of 1/3 of the iliac apophysis ossification. The second study was a retrospective case control study. It showed the potential for 3D parameters to help predict the evolution. 3D spinal parameters at first visit of a group of patient eventually treated with surgery and a group who had no progression revealed statistical differences for: mean 3D wedging of the apical disks, lower junctional vertebral axial rotation, torsion and T6 and whole spine height/width ratio were all significantly affected. The last study was a prospective cohort study based on an adolescent idiopathic scoliosis group followed from first visit to skeletal maturity. A general linear model was developed based on 3D spinal parameters and on curve type, Cobb angle at first visit and with the 3 stages skeletal maturity system developed in the first study. The predictive model obtained has a determination coefficient of 0,715. Included 3D parameters predictors were: the angle of the plane of maximal curvature, the 3D wedging of T3-­T4, T8-­T9 and T11-­T12 disks, and the sum of 3D wedging of all thoracic and lumbar disks. The predictive model developed reinforced the importance of considering adolescent idiopathic scoliosis in a three-­‐dimensional point of view. This model will also optimise the prediction of evolution at first visit.