Operators on a manifold with (geometric) singularities are degenerate in a natural way. They have a principal symbolic structure with contributions from the different strata of the configuration. We study the calculus of such operators on the level of edge symbols of second generation, based on specific quantizations of the corner-degenerate interior symbols, and show that this structure is preserved under compositions.

Statistical models are often used for the prediction of future random variables. There are two types of prediction, point prediction and probabilistic prediction. The prediction accuracy is quantified by performance measures, which are typically based on loss functions. We study the estimators of these performance measures, the prediction error and performance scores, for point and probabilistic predictors, respectively. The focus of this thesis is to assess the prediction performance of survival models that analyze censored survival times. To accommodate censoring, we extend the inverse probability censoring weighting (IPCW) method, thus arbitrary loss functions can be handled. We also develop confidence interval procedures for these performance measures. We compare model-based, apparent loss based and cross-validation estimators of prediction error under model misspecification and variable selection, for absolute relative error loss (in chapter 3) and misclassification error loss (in chapter 4). Simulation results indicate that cross-validation procedures typically produce reliable point estimates and confidence intervals, whereas model-based estimates are often sensitive to model misspecification. The methods are illustrated for two medical contexts in chapter 5. The apparent loss based and cross-validation estimators of performance scores for probabilistic predictor are discussed and illustrated with an example in chapter 6. We also make connections for performance.

Statistical models are often used for the prediction of future random variables. There are two types of prediction, point prediction and probabilistic prediction. The prediction accuracy is quantified by performance measures, which are typically based on loss functions. We study the estimators of these performance measures, the prediction error and performance scores, for point and probabilistic predictors, respectively. The focus of this thesis is to assess the prediction performance of survival models that analyze censored survival times. To accommodate censoring, we extend the inverse probability censoring weighting (IPCW) method, thus arbitrary loss functions can be handled. We also develop confidence interval procedures for these performance measures. We compare model-based, apparent loss based and cross-validation estimators of prediction error under model misspecification and variable selection, for absolute relative error loss (in chapter 3) and misclassification error loss (in chapter 4). Simulation results indicate that cross-validation procedures typically produce reliable point estimates and confidence intervals, whereas model-based estimates are often sensitive to model misspecification. The methods are illustrated for two medical contexts in chapter 5. The apparent loss based and cross-validation estimators of performance scores for probabilistic predictor are discussed and illustrated with an example in chapter 6. We also make connections for performance.

A recent debate has identified a description– experience gap, where the non-linear weighting function identified in prospect theory reverses when probabilities are discovered through experience rather than by description (probabilities). This thesis will explore the role of experience and probabilities theoretically and empirically. It is argued that both behaviors are compatible on a theoretical basis given a preference for the status quo, but produce opposing decision weights due to different cognitive and motivational factors. Probabilities focus a decision on the potential for rare events creating a preference for certain outcomes and reduced risk taking consistent with loss aversion. Experience overweighs customary outcomes consistent with sensitivity to a reference point or the status quo. Experience in the form of loss, however, moderates the effect of probabilities on risk taking. An experimental game of dice supports this hypothesis, suggesting ambiguity seeking in the face of loss and raising the possibility that the use of probabilities may not be always be maximizing behavior.

Preliminary normative standards are a tool clinical exercise specialists and health fitness instructors can use when interpreting muscular strength testing results. However, a challenge for professionals is evaluating an individual's one-repetition maximum (IRM) and relating that to others of the same age and gender, because there are no preliminary normative standards for 1RMs available when testing via free-weights and machines.This study conducted at Ball State University, Adult Physical Fitness Laboratory, examined results of muscular strength testing in order to obtain the normative muscular strength of adults. The purpose was to develop preliminary normative standards for strength of adults and to compare the 1RM weight an individual lifts between free-weights, Paramount, and Cybex machines. Seventy-nine healthy men and women between 18 and 79 years of age participated in the study. Subjects were tested on free weights, Paramount, and Cybex machines.Test results revealed preliminary normative standards for 1RM on free weights. Individuals were categorized in three age groups for the free-weight bench press and the Cybex (free-weight) Leg Press. The 18-23 year olds obtained a IRM mean (± Standard Deviation (SD)) of 200.6 + 32.8 lbs and 83.6 ± 18.5 lbs for men and women, respectively, for the free-weight bench press. The 43-59 year olds obtained a 1RM mean of 149.2 ± 41.8 lbs and 71.3 ± 8.6 lbs and the 60-79 year olds had a 1RM mean of 119.5 + 30.0 Ibs and 61.6 ± 15.6 lbs for men and women, respectively, for the free-weight bench press. The 18-23 year olds obtained a 1RM Cybex (free-weight) leg press mean of 484.9 + 58.0 lbs and 234.3 ± 67.5 lbs for men and women, respectively. The 43-59 year olds were able to obtain 1RM means of 444.4 + 84.9 lbs and 254.5 ± 51.7 lbs and the older subjects (60-79 years old) were able to obtain 1RM mean of 390.7 ± 98.6 lbs and 230.3 ± 76.6 lbs for men and women, respectively. Results were also documented in relative values by the amount of weight pushed divided by body weight for better comparison of individuals. Subjects generally lifted more weight on the Cybex (free-weight) leg press compared to the Cybex (machine) leg press. All subjects (N=79) had a mean and standard deviation of 294.9 + 87.7 lbs for the Cybex (machine) leg press (1RMs) and 343.4 ± 123.4 lbs on the Cybex (free-weight) leg press (1RMs). There was a significant difference between the Cybex (free-weight) leg press and the Cybex leg press (p<.001). The correlation for these two types of lifts was r=0.88. There was a significant difference between the free-weight bench press and the Paramount seated chest press (p<.001). The correlation for between the two types of lifts was r=0.93. / School of Physical Education, Sport, and Exercise Science

In this thesis we develop a theoretical framework for the identification of situations where the equal frequency (EF) or equal variance (EV) subclassification may produce lower bias and/or variance of the estimator. We conduct simulation studies to examine the EF and EV approaches under different types of model misspecification. We apply two weighting schemes in our simulations: equal weights (EW) and inverse variance (IV) weights. Our simulation results indicate that under the quadratic term misspecification, the EF-IV estimator provides the lowest bias and root mean square error as compared to the ordinary least square estimator and other propensity score estimators. Our theorem development demonstrates that if higher variation occurs with larger bias for within subclass treatment effect estimates then the EF-IV estimator has a smaller overall bias than the EF-EW estimator. We show that the EF-IV estimator always has a smaller variance than the EF-EW estimator. We also propose a novel method of subclassification that focuses on creating homogeneous propensity score subclasses to produce an estimator with reduced biased in some circumstances. We feel our research contributes to the field of propensity score adjustments by providing new theorems to compare the overall bias and variance between different propensity score estimators. / Graduation date: 2012

Diss. (sammanfattning) Stockholm : Karol. inst., 2004. / Härtill 4 uppsatser.

Thesis (Ph. D.)--Earth and Atmospheric Sciences, Georgia Institute of Technology, 2006. / Michael Bergin, Committee Member ; E. Michael Perdue, Committee Chair ; Ching-Hua Huang, Committee Member ; Ellery Ingall, Committee Member ; Martial Taillefert, Committee Member. Vita. Includes bibliographical references.

SOUSA FILHO, Severino Cavalcante de. Estimativas de funções de covariância para características de crescimento da raça tabapuã utilizando modelo de regressão aleatória. 2007. 53 f. : Dissertação (Mestrado) - Universidade Federal do Ceará, Centro de Ciências, Departamento de Zootecnia, Programa de Pós-Graduação em Zootecnia. Fortaleza-CE, 2007. / Submitted by Eric Santiago (erichhcl@gmail.com) on 2016-08-10T13:04:58Z No. of bitstreams: 1 2007_dis_scsousajunior.pdf: 275473 bytes, checksum: ea65f4f3ad2f575a496e925cccf3923a (MD5) / Approved for entry into archive by Nádja Goes (nmoraissoares@gmail.com) on 2016-08-10T15:18:04Z (GMT) No. of bitstreams: 1 2007_dis_scsousajunior.pdf: 275473 bytes, checksum: ea65f4f3ad2f575a496e925cccf3923a (MD5) / Made available in DSpace on 2016-08-10T15:18:04Z (GMT). No. of bitstreams: 1 2007_dis_scsousajunior.pdf: 275473 bytes, checksum: ea65f4f3ad2f575a496e925cccf3923a (MD5) Previous issue date: 2007 / The study used 28,873 weight records taken along the life of 6.471 animals of the race Tabapuã, finery birth to 660 days of age, belonging to the animal archives of the Brazilian Association of Zebu Breeders (ABCZ) to estimate the covariânce functions using the models of random regression. The genetic, addictive direct an permanent environmental effects were used as random effects the contemporary groups as fixed effects. The average age of the cows at delivery as covariavel (linear and quadratic). The residue was modeled by functions of variances of quadratic order. The analyses with orthogonal polynomials were performed for the direct genetic effect, genetic of animal permanent environment atmosphere of linear and quadratic. Models were compared by the Bayesian of information criteria of Schwarz (BIC) and of Akaike (AIC). The heritability estimates for the direct effects were greater in the beginning and by the end of the studied period, with values of 0,48 at birth, 0,27 to the 240 days and 0,14 to the 660 days of age. The genetic correlations varied from moderate to high, reducing as intensity in proportion to the increase of the increase of distance between ages the distance accordingly among the ages. / Utilizou-se 28.873 registros de pesos do quinto aos 660 dias de idade de 6.471 animais da raça Tabapuã, pertencentes ao arquivo do Controle do Desenvolvimento Ponderal da Associação Brasileira dos Criadores de Zebu (ABCZ) para estimar as funções de covariância utilizando modelo de regressão aleatória. Foram empregados como aleatórios os efeitos genético, aditivo direto e materno de ambiente permanente de animal e materno e como efeitos fixos foram considerados os grupos contemporâneos, a idade média das vacas ao parto como covariável. O resíduo foi modelado por funções de variâncias de ordem quíntinca. As análises com polinômios ortogonais foram realizadas para o efeito genético aditivo direto, ambiente permanente de animal e segundo efeito de animal (ambiente permanente materno e efeito materno) de ordens 4,5,2 e 3 respectivamnte. Os modelos foram comparados pelos critérios de informação Bayesiano de Schwarz (BIC) e de Akaike (AIC). As estimativas de herdabilidade para os efeitos diretos apresentam decréscimo do nascimento até a desmama e apresenta um leve aumento após a desmama para novamente tender a decrescer, com valores de 0,48 ao nascimento; 0,27 aos 240 dias e 0,14 aos 660 dias de idade. As correlações genéticas variaram de moderadas a altas, diminuindo conforme o aumento da distância entre as idades.

La modélisation structurée de préférences, fondée sur les notions d'indépendance préférentielle, a un potentiel énorme pour fournir des approches efficaces pour la représentation et le raisonnement sur les préférences des décideurs dans les applications de la vie réelle. Cette thèse soulève la question de la représentation des préférences par une structure graphique. Nous proposons une nouvelle lecture de réseaux possibilistes, que nous appelons p-pref nets, où les degrés de possibilité représentent des degrés de satisfaction. L'approche utilise des poids de possibilité non instanciés (appelés poids symboliques), pour définir les tables de préférences conditionnelles. Ces tables donnent naissance à des vecteurs de poids symboliques qui codent les préférences qui sont satisfaites et celles qui sont violées dans un contexte donné. Nous nous concentrons ensuite sur les aspects théoriques de la manipulation de ces vecteurs. En effet, la comparaison de ces vecteurs peut s'appuyer sur différentes méthodes: celles induites par la règle de chaînage basée sur le produit ou celle basée sur le minimum que sous-tend le réseau possibiliste, les raffinements du minimum le discrimin, ou leximin, ainsi que l'ordre Pareto, et le Pareto symétrique qui le raffine. Nous prouvons que la comparaison par produit correspond exactement au celle du Pareto symétrique et nous nous concentrons sur les avantages de ce dernier par rapport aux autres méthodes. En outre, nous montrons que l'ordre du produit est consistant avec celui obtenu en comparant des ensembles de préférences satisfaites des tables. L'image est complétée par la proposition des algorithmes d'optimisation et de dominance pour les p-pref nets. Dans ce travail, nous discutons divers outils graphiques pour la représentation des préférences. Nous nous focalisons en particulier sur les CP-nets car ils partagent la même structure graphique que les p-pref nets et sont basés sur la même nature de préférences. Nous prouvons que les ordres induits par les CP-nets ne peuvent pas contredire ceux des p-pref nets et nous avons fixé les contraintes nécessaires pour raffiner les ordres des p-pref nets afin de capturer les contraintes Ceteris Paribus des CP-nets. Cela indique que les CP-nets représentent potentiellement une sous-classe des p-pref nets avec des contraintes. Ensuite, nous fournissons une comparaison approfondie entre les différents modèles graphiques qualitatifs et quantitatifs, et les p-pref nets. Nous en déduisons que ces derniers peuvent être placés à mi- chemin entre les modèles qualitatifs et les modèles quantitatifs puisqu'ils ne nécessitent pas une instanciation complète des poids symboliques alors que des informations supplémentaires sur l'importance des poids peuvent être prises en compte. La dernière partie de ce travail est consacrée à l'extension du modèle proposé pour représenter les préférences de plusieurs agents. Dans un premier temps, nous proposons l'utilisation de réseaux possibilistes où les préférences sont de type tout ou rien et nous définissons le conditionnement dans le cas de distributions booléennes. Nous montrons par ailleurs que ces réseaux multi-agents ont une contrepartie logique utile pour vérifier la cohérence des agents. Nous expliquons les étapes principales pour transformer ces réseaux en format logique. Enfin, nous décrivons une extension pour représenter des préférences nuancées et fournissons des algorithmes pour les requêtes d'optimisation et de dominance. / Structured modeling of preference statements, grounded in the notions of preferential independence, has tremendous potential to provide efficient approaches for modeling and reasoning about decision maker preferences in real-life applications. This thesis raises the question of representing preferences through a graphical structure. We propose a new reading of possibilistic networks, that we call p-pref nets, where possibility weights represent satisfaction degrees. The approach uses non-instantiated possibility weights, which we call symbolic weights, to define conditional preference tables. These conditional preference tables give birth to vectors of symbolic weights that reflect the preferences that are satisfied and those that are violated in a considered situation. We then focus on the theoretical aspects of handling of these vectors. Indeed, the comparison of such vectors may rely on different orderings: the ones induced by the product-based, or the minimum based chain rule underlying the possibilistic network, the discrimin, or leximin refinements of the minimum- based ordering, as well as Pareto ordering, and the symmetric Pareto ordering that refines it. We prove that the product-based comparison corresponds exactly to symmetric Pareto and we focus on its assets compared to the other ordering methods. Besides, we show that productbased ordering is consistent with the ordering obtained by comparing sets of satisfied preference tables. The picture is then completed by the proposition of algorithms for handling optimization and dominance queries. In this work we discuss various graphical tools for preference representation. We shed light particularly on CP-nets since they share the same graphical structure as p-pref nets and are based on the same preference statements. We prove that the CP-net orderings cannot contradict those of the p-pref nets and we found suitable additional constraints to refine p-pref net orderings in order to capture Ceteris Paribus constraints of CP-nets. This indicates that CP-nets potentially represent a subclass of p-pref nets with constraints. Finally, we provide an thorough comparison between the different qualitative and quantitative graphical models and p-pref nets. We deduce that the latter can be positioned halfway between qualitative and quantitative models since they do not need a full instantiation of the symbolic weights while additional information about the relative strengths of these weights can be taken into account. The last part of this work is dedicated to extent the proposed model to represent multiple agents preferences. As a first step, we propose the use of possibilistic networks for representing all or nothing multiple agents preferences and define conditioning in the case of Boolean possibilities. These multiple agents networks have a logical counterpart helpful for checking agents consistency. We explain the main steps for transforming multiple agents networks into logical format. Finally, we outline an extension with priority levels of these networks and provide algorithms for handling optimization and dominance queries.