This thesis presents novel, robust, analytic and algorithmic methods for calculating Bayesian posterior intervals of receiver operating characteristic (ROC) curves and confusion matrices used for the evaluation of intelligent medical systems tested with small amounts of data. Intelligent medical systems are potentially important in encapsulating rare and valuable medical expertise and making it more widely available. The evaluation of intelligent medical systems must make sure that such systems are safe and cost effective. To ensure systems are safe and perform at expert level they must be tested against human experts. Human experts are rare and busy which often severely restricts the number of test cases that may be used for comparison. The performance of expert human or machine can be represented objectively by ROC curves or confusion matrices. ROC curves and confusion matrices are complex representations and it is sometimes convenient to summarise them as a single value. In the case of ROC curves, this is given as the Area Under the Curve (AUC), and for confusion matrices by kappa, or weighted kappa statistics. While there is extensive literature on the statistics of ROC curves and confusion matrices they are not applicable to the measurement of intelligent systems when tested with small data samples, particularly when the AUC or kappa statistic is high. A fundamental Bayesian study has been carried out, and new methods devised, to provide better statistical measures for ROC curves and confusion matrices at low sample sizes. They enable exact Bayesian posterior intervals to be produced for: (1) the individual points on a ROC curve; (2) comparison between matching points on two uncorrelated curves; . (3) the AUC of a ROC curve, using both parametric and nonparametric assumptions; (4) the parameters of a parametric ROC curve; and (5) the weight of a weighted confusion matrix. These new methods have been implemented in software to provide a powerful and accurate tool for developers and evaluators of intelligent medical systems in particular, and to a much wider audience using ROC curves and confusion matrices in general. This should enhance the ability to prove intelligent medical systems safe and effective and should lead to their widespread deployment. The mathematical and computational methods developed in this thesis should also provide the basis for future research into determination of posterior intervals for other statistics at small sample sizes.

Thesis (M.S.)--Georgia State University, 2008. / Title from file title page. Gengsheng Qin, committee chair; Yu-Sheng Hsu, Yixin Fang, Yuanhui Xiao, committee members. Description based on contents viewed July 22, 2009. Includes bibliographical references (p. 29-30).

In the medical science, the receiving operationg characteristic (ROC) curve is a graphical representation to evaluate the accuracy of a medical diagnostic test for any cut-off point. The area under the ROC curve (AUC) is an overall performance measure for a diagnostic test. There are two parts in this dissertation. In the first part, we study the properties of bi-Exponentiated Weibull models. FIrst, we derive a general moment formula for single Exponentiated Weibull models. Then we move on to derive the precise formula of AUC and study the maximus likelihood estimation (MLE) of the AUC. Finally, we obtain the asymptotoc distribution of the estimated AUC. Simulation studies are used to check the performance of MLE of AUC under the moderate sample sizes. The second part fo the dissertation is to study the estimation of AUC under the crossing model, which extends the AUC formula in Gonen and Heller (2007). / by Fazhe Chang. / Thesis (Ph.D.)--Florida Atlantic University, 2012. / Includes bibliography. / Mode of access: World Wide Web. / System requirements: Adobe Reader.

<p>Many geotechnical engineering problems involve combining two or more independent physical processes as a coupled solution of seepage, volume change and shear strength. For any physical process being modeled, it is desirous to be able to compute any of the volume-mass soil properties. When the volume-mass soil properties are combined with the stress state of the soil, the result is a volume-mass constitutive relationship. Three volume-mass constitutive relationships (i.e., void ratio, water content and degree of saturation) are generally viewed as being the most fundamental; however, only two of the relations are independent. The unsaturated soil properties associated with seepage, volume change and shear strength problems are also related to the volume-mass soil properties. While the unsaturated soil properties are often estimated as simply being a function of the soil-water characteristic curve, it is more accurate to define the properties in a more rigorous manner in terms of the volume-mass soil properties. The advancement of computing capabilities means that it is quite easy to formulate constitutive relations for shear strength and permeability, for example, in terms of all volume-mass properties of the unsaturated soil.</p><p>The objectives of this dissertation include: i) the development of volume-mass constitutive models for unsaturated soils; ii) the further study and verification of the volume-mass constitutive behavior of unsaturated soils; and iii) the development of techniques for visualization of volume-mass constitutive surfaces for unsaturated soils. To achieve these objectives, the present research study was conducted from both theoretical and experimental bases.</p><p>The theoretical program commenced with a comprehensive literature review of the volume-mass constitutive relationships for unsaturated soils. A new, more rigorous volume-mass constitutive model was then proposed. Appropriate terminology was introduced for the development of the model, followed by an outline of the assumptions used and the mathematical derivation. The proposed model requires conventionally obtainable soil properties for its calibration. The model is capable of predicting both the void ratio and water content constitutive relationships for various unsaturated soils, taking into account elastic and plastic volume changes. Various stress paths can be simulated and hysteresis associated with the soil-water characteristic curve can be taken into account. </p><p>Two closed-form equations for the volume-mass constitutive relationships were derived. A computer software program was written based on the theory of the proposed volume-mass constitutive model. Techniques for the visualization of the volume-mass constitutive surfaces were then presented. An experimental program was conducted in the laboratory. The experimental program involved the verification of a new testing apparatus. Several soils were selected for testing purposes and appropriate testing procedures were established (i.e., soil specimens were initially slurry). The testing stress paths followed in the experimental program were different from most research programs conducted in the past and reported in the research literature. Conclusions regarding the compressibility, stress path dependency, and hysteretic nature of the soil-water characteristic curve of an unsaturated soil were presented.</p><p>A considerable number of test results (i.e., from both the experimental program and the research literature) were used in the verification of the new volume-mass constitutive model. This model has proven to be effective in predicting both collapse and expansion of a soil. The volume-mass constitutive model appears to predict behaviour in a satisfactory manner for a wide range of soils; however, the predictions appear to be superior for certain soils. In all cases the volume-mass predictions of the model appear to be satisfactory for geotechnical engineering practice.

<p>Many geotechnical engineering problems involve combining two or more independent physical processes as a coupled solution of seepage, volume change and shear strength. For any physical process being modeled, it is desirous to be able to compute any of the volume-mass soil properties. When the volume-mass soil properties are combined with the stress state of the soil, the result is a volume-mass constitutive relationship. Three volume-mass constitutive relationships (i.e., void ratio, water content and degree of saturation) are generally viewed as being the most fundamental; however, only two of the relations are independent. The unsaturated soil properties associated with seepage, volume change and shear strength problems are also related to the volume-mass soil properties. While the unsaturated soil properties are often estimated as simply being a function of the soil-water characteristic curve, it is more accurate to define the properties in a more rigorous manner in terms of the volume-mass soil properties. The advancement of computing capabilities means that it is quite easy to formulate constitutive relations for shear strength and permeability, for example, in terms of all volume-mass properties of the unsaturated soil.</p><p>The objectives of this dissertation include: i) the development of volume-mass constitutive models for unsaturated soils; ii) the further study and verification of the volume-mass constitutive behavior of unsaturated soils; and iii) the development of techniques for visualization of volume-mass constitutive surfaces for unsaturated soils. To achieve these objectives, the present research study was conducted from both theoretical and experimental bases.</p><p>The theoretical program commenced with a comprehensive literature review of the volume-mass constitutive relationships for unsaturated soils. A new, more rigorous volume-mass constitutive model was then proposed. Appropriate terminology was introduced for the development of the model, followed by an outline of the assumptions used and the mathematical derivation. The proposed model requires conventionally obtainable soil properties for its calibration. The model is capable of predicting both the void ratio and water content constitutive relationships for various unsaturated soils, taking into account elastic and plastic volume changes. Various stress paths can be simulated and hysteresis associated with the soil-water characteristic curve can be taken into account. </p><p>Two closed-form equations for the volume-mass constitutive relationships were derived. A computer software program was written based on the theory of the proposed volume-mass constitutive model. Techniques for the visualization of the volume-mass constitutive surfaces were then presented. An experimental program was conducted in the laboratory. The experimental program involved the verification of a new testing apparatus. Several soils were selected for testing purposes and appropriate testing procedures were established (i.e., soil specimens were initially slurry). The testing stress paths followed in the experimental program were different from most research programs conducted in the past and reported in the research literature. Conclusions regarding the compressibility, stress path dependency, and hysteretic nature of the soil-water characteristic curve of an unsaturated soil were presented.</p><p>A considerable number of test results (i.e., from both the experimental program and the research literature) were used in the verification of the new volume-mass constitutive model. This model has proven to be effective in predicting both collapse and expansion of a soil. The volume-mass constitutive model appears to predict behaviour in a satisfactory manner for a wide range of soils; however, the predictions appear to be superior for certain soils. In all cases the volume-mass predictions of the model appear to be satisfactory for geotechnical engineering practice.

The purpose of the present study is to investigate the predictive validity of the BUEPE through the use of the three-parameter IRT model&amp / #8217 / s ability estimates. The study made use of the BUEPE September 2000 data which included the responses of 699 students. The predictive validity was established by using the departmental English courses (DEC) passing grades of a total number of 371 students. As for the prerequisite analysis the best fitted model of IRT was determined by first, checking the assumptions of IRT / second, by analyzing the invariance of ability parameters and item parameters and thirdly, by interpreting the chi-square statistics. After the prerequisite analyses, the best fitted model&amp / #8217 / s estimates were correlated with DEC passing grades to investigate the predictive power of BUEPE on DEC passing grades. The findings indicated that the minimal guessing assumption of the one- and two-parameter models was not met. In addition, the chi-square statistics indicated a better fit to the three-parameter model. Therefore, it was concluded that the best fitted model was the three-parameter model. The findings of the predictive validity analyses revealed that the best predictors for DEC passing grades were the three-parameter model ability estimates. The second best predictor was the ability estimates obtained from sixty high information items. In the third place BUEPE total scores and the total scores obtained from sixty high information items followed with nearly the same correlation coefficients. Among the three sub-tests, the reading sub-test was found to be the best predictor of DEC passing grades.

A problemática associada à execução e interpretação de ensaios de campo (e.g. palheta e pizocone) em materiais siltosos motiva a presente pesquisa, onde são desenvolvidas modelagens analíticas em poroelasticidade para o estudo do efeito de fluxo transiente no solo. As modelagens desenvolvidas referem-se aos problemas de rotação e expansão de um cilindro inserido na massa de solo. A abordagem adotada para solução dos problemas baseia-se na equivalência entre a resposta local de um comportamento perfeitamente plástico, em processo de carregamento monotônico, e um comportamento fictício não-linear poroelástico apropriado. Soluções fechadas para o campo de tensões, deformações e poropressões foram obtidas para o problema simplificado de rotação. Para a solução do problema de expansão considerou-se que um módulo equivalente elástico condiciona o fluxo, o que possibilita a obtenção de uma solução fechada para as distribuições de poropressões, tensões e deformações foram calculadas numericamente. Os modelos desenvolvidos foram criticamente comparados a resultados de simulações numéricas em elementos finitos, demostrando capturar a mesma tendência de comportamento. As condições de drenagem foram interpretadas no espaço de velocidade normalizada V e grau de drenagem U, demostrando que o processo de dissipação é sensível à rigidez do material. Uma tentativa de aplicação dos modelos foi realizada para a interpretação de ensaios de palheta em resíduo de zinco, e piezocone em resíduo de ouro. Destaca-se que as aplicações propostas não são determinísticas, e foram utilizadas para identificação de padrões de comportamento e análise de sensibilidade de parâmetros. Neste contexto, verificou-se que os modelos podem ser utilizados para a estimativa das velocidades não drenadas de ensaio, porém a transição de comportamento parcialmente drenado para drenado é subestimada pelos modelos. Por fim observa-se que, de maneira geral, os modelos se demonstram úteis para o entendimento do comportamento de materiais siltosos em fluxo transiente. / The problems associated with the in situ tests interpretation in silty materials motivates the present research where analytical models were developed for the study of transient flow. The developed models refer to the rotation and expansion of a cylinder considered deeply embedded into an infinite nonlinear poroelastic medium. The approach is based on the local equivalence between the response of a perfectly plastic behavior to monotonic loading and an appropriate fictitious non-linear poroelastic response. Closed-form solutions for pore pressures, stresses and displacements were derived for the rotation problem within a simplified poroelastic framework. The expansion problem was solved considering a simplified framework for the diffusion equation to derive a closed-form expression for pore pressure distribution, while stresses and displacements were computed numerically. The results are discretised and critically compared to finite element solutions showing good agreement in terms of radial stresses and pore pressure distributions. Results are also displayed in the space of normalized velocity (V) versus degree of drainage (U), showing to be sensitive to the soil rigidity. An attempt to apply the models was made: a) for the interpretation of vane tests in zinc tailings; b) for the interpretation of piezocone tests in gold tailings. Applications are considered approximate, showing that the models can be used to estimate the onset of the undrained regime, wheres the transition from partially drained to drained is underestimated by the models. In general, the models prove to be useful in understanding rate effects in silty soils.

A problemática associada à execução e interpretação de ensaios de campo (e.g. palheta e pizocone) em materiais siltosos motiva a presente pesquisa, onde são desenvolvidas modelagens analíticas em poroelasticidade para o estudo do efeito de fluxo transiente no solo. As modelagens desenvolvidas referem-se aos problemas de rotação e expansão de um cilindro inserido na massa de solo. A abordagem adotada para solução dos problemas baseia-se na equivalência entre a resposta local de um comportamento perfeitamente plástico, em processo de carregamento monotônico, e um comportamento fictício não-linear poroelástico apropriado. Soluções fechadas para o campo de tensões, deformações e poropressões foram obtidas para o problema simplificado de rotação. Para a solução do problema de expansão considerou-se que um módulo equivalente elástico condiciona o fluxo, o que possibilita a obtenção de uma solução fechada para as distribuições de poropressões, tensões e deformações foram calculadas numericamente. Os modelos desenvolvidos foram criticamente comparados a resultados de simulações numéricas em elementos finitos, demostrando capturar a mesma tendência de comportamento. As condições de drenagem foram interpretadas no espaço de velocidade normalizada V e grau de drenagem U, demostrando que o processo de dissipação é sensível à rigidez do material. Uma tentativa de aplicação dos modelos foi realizada para a interpretação de ensaios de palheta em resíduo de zinco, e piezocone em resíduo de ouro. Destaca-se que as aplicações propostas não são determinísticas, e foram utilizadas para identificação de padrões de comportamento e análise de sensibilidade de parâmetros. Neste contexto, verificou-se que os modelos podem ser utilizados para a estimativa das velocidades não drenadas de ensaio, porém a transição de comportamento parcialmente drenado para drenado é subestimada pelos modelos. Por fim observa-se que, de maneira geral, os modelos se demonstram úteis para o entendimento do comportamento de materiais siltosos em fluxo transiente. / The problems associated with the in situ tests interpretation in silty materials motivates the present research where analytical models were developed for the study of transient flow. The developed models refer to the rotation and expansion of a cylinder considered deeply embedded into an infinite nonlinear poroelastic medium. The approach is based on the local equivalence between the response of a perfectly plastic behavior to monotonic loading and an appropriate fictitious non-linear poroelastic response. Closed-form solutions for pore pressures, stresses and displacements were derived for the rotation problem within a simplified poroelastic framework. The expansion problem was solved considering a simplified framework for the diffusion equation to derive a closed-form expression for pore pressure distribution, while stresses and displacements were computed numerically. The results are discretised and critically compared to finite element solutions showing good agreement in terms of radial stresses and pore pressure distributions. Results are also displayed in the space of normalized velocity (V) versus degree of drainage (U), showing to be sensitive to the soil rigidity. An attempt to apply the models was made: a) for the interpretation of vane tests in zinc tailings; b) for the interpretation of piezocone tests in gold tailings. Applications are considered approximate, showing that the models can be used to estimate the onset of the undrained regime, wheres the transition from partially drained to drained is underestimated by the models. In general, the models prove to be useful in understanding rate effects in silty soils.

A problemática associada à execução e interpretação de ensaios de campo (e.g. palheta e pizocone) em materiais siltosos motiva a presente pesquisa, onde são desenvolvidas modelagens analíticas em poroelasticidade para o estudo do efeito de fluxo transiente no solo. As modelagens desenvolvidas referem-se aos problemas de rotação e expansão de um cilindro inserido na massa de solo. A abordagem adotada para solução dos problemas baseia-se na equivalência entre a resposta local de um comportamento perfeitamente plástico, em processo de carregamento monotônico, e um comportamento fictício não-linear poroelástico apropriado. Soluções fechadas para o campo de tensões, deformações e poropressões foram obtidas para o problema simplificado de rotação. Para a solução do problema de expansão considerou-se que um módulo equivalente elástico condiciona o fluxo, o que possibilita a obtenção de uma solução fechada para as distribuições de poropressões, tensões e deformações foram calculadas numericamente. Os modelos desenvolvidos foram criticamente comparados a resultados de simulações numéricas em elementos finitos, demostrando capturar a mesma tendência de comportamento. As condições de drenagem foram interpretadas no espaço de velocidade normalizada V e grau de drenagem U, demostrando que o processo de dissipação é sensível à rigidez do material. Uma tentativa de aplicação dos modelos foi realizada para a interpretação de ensaios de palheta em resíduo de zinco, e piezocone em resíduo de ouro. Destaca-se que as aplicações propostas não são determinísticas, e foram utilizadas para identificação de padrões de comportamento e análise de sensibilidade de parâmetros. Neste contexto, verificou-se que os modelos podem ser utilizados para a estimativa das velocidades não drenadas de ensaio, porém a transição de comportamento parcialmente drenado para drenado é subestimada pelos modelos. Por fim observa-se que, de maneira geral, os modelos se demonstram úteis para o entendimento do comportamento de materiais siltosos em fluxo transiente. / The problems associated with the in situ tests interpretation in silty materials motivates the present research where analytical models were developed for the study of transient flow. The developed models refer to the rotation and expansion of a cylinder considered deeply embedded into an infinite nonlinear poroelastic medium. The approach is based on the local equivalence between the response of a perfectly plastic behavior to monotonic loading and an appropriate fictitious non-linear poroelastic response. Closed-form solutions for pore pressures, stresses and displacements were derived for the rotation problem within a simplified poroelastic framework. The expansion problem was solved considering a simplified framework for the diffusion equation to derive a closed-form expression for pore pressure distribution, while stresses and displacements were computed numerically. The results are discretised and critically compared to finite element solutions showing good agreement in terms of radial stresses and pore pressure distributions. Results are also displayed in the space of normalized velocity (V) versus degree of drainage (U), showing to be sensitive to the soil rigidity. An attempt to apply the models was made: a) for the interpretation of vane tests in zinc tailings; b) for the interpretation of piezocone tests in gold tailings. Applications are considered approximate, showing that the models can be used to estimate the onset of the undrained regime, wheres the transition from partially drained to drained is underestimated by the models. In general, the models prove to be useful in understanding rate effects in silty soils.

We investigate in this thesis the generic properties of curves in the Minkowski plane R2 1 and of smooth Lorentzian surfaces. The generic properties of curves in R2 1 are obtained by studying the contacts of curves in R2 1 with lines and pseudo-circles. These contacts are captured by the singularities of the families of height and distancesquared functions on the curves. On the other hand, the generic properties of smooth Lorentzian surfaces are obtained by studying certain Binary Differential Equations defined on the surfaces.