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Latent variables are often included in a model in order to capture the diversity among subjects in a population. Sometimes the distribution of these latent variables are of principle interest. In studies where sequences of observations are taken from subjects, ancillary variables, such as the number of observations provided by each subject, usually also vary between subjects. The goal here is to understand efficient estimation of the expectation of the latent variable in the presence of these subject-specific ancillaries. Unbiased estimation and efficient estimation of the expectation of the latent parameter depend on the dependence structure of these three subject-specific components: latent variable, sequence of observations, and ancillary. This dissertation considers estimation under two dependence configurations. In Chapter 3, efficiency is studied under the model in which no assumptions are made about the joint distribution of the latent variable and the subject-specific ancillary. Chapter 4 treats the setting where the ancillary variable and the latent variable are independent.

Xu Liang. / "June 2002." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (p. 74-82). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

Tsang, Yim Fan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (leaves 48). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Background of the Latent Normal Model and the Latent Growth Curve Model --- p.4 / Chapter 2.1 --- Latent. Variable Growth Curve Modeling --- p.5 / Chapter 2.1.1 --- Two-factor Latent Variable Growth Curve Model for Two Time Points --- p.5 / Chapter 2.1.2 --- The Intercept and Slope Factors --- p.7 / Chapter 2.1.3 --- The Factor Loadings of the Slope Factor --- p.8 / Chapter 2.1.4 --- The Error Variance --- p.9 / Chapter 2.1.5 --- "Expressing Model Parameters as Functions of Measured Means, Variances and Covariances" --- p.10 / Chapter 2.2 --- Maximum Likelihood Estimation of the Latent Normal Model from Ordinal Data --- p.12 / Chapter 2.2.1 --- Model --- p.13 / Chapter 2.2.2 --- The Maximum Likelihood Estimation Function --- p.15 / Chapter 2.2.3 --- Derivation of the Likelihood Equations --- p.16 / Chapter 2.3 --- The Two Approaches for Generalizing the Latent Normal Model for Analyzing Latent Growth Curve Model --- p.17 / Chapter 3 --- Latent Variable Growth Curve Modeling for Ordinal Categorical Data --- p.19 / Chapter 3.1 --- The Model and the Maximum Likelihood Estimation --- p.20 / Chapter 3.1.1 --- The Two-factor Growth Curve Model with Ordinal Variables --- p.20 / Chapter 3.1.2 --- Implementation --- p.23 / Chapter 3.2 --- The Two-Stage Estimation Method --- p.28 / Chapter 3.2.1 --- Maximum Likelihood Estimation of the Latent Normal Method --- p.28 / Chapter 3.2.2 --- Two-factor Latent Growth Curve Model --- p.29 / Chapter 3.3 --- Misleading Result of Using Continuous Assumption for Ordinal Categorical Data --- p.31 / Chapter 3.3.1 --- Latent Growth Curve Modeling Method --- p.32 / Chapter 3.3.2 --- Direct Continuous Assumption to the Ordinal Categorical Data --- p.33 / Chapter 3.3.3 --- Interpretation --- p.35 / Chapter 3.4 --- Simulation Study --- p.36 / Chapter 4 --- Conclusion --- p.40 / Appendices --- p.43 / A Sample Mx Input Script for Latent Growth Curve Analysis of Ordinal Categorical Data --- p.43

L’information quantique peut être traitée de deux manières fondamentalement différentes: à l’aide de variables discrètes ou continues. Dans cette thèse, nous étudions de manière théorique la réalisation de protocoles d’information quantique dans les systèmes caractérisés par des variables continues. Pour ce faire, nous utilisons les variables modulaires comme outil afin de révéler des structures discrètes dans les états, opérations et observables. Le présent travail est fortement motivé par l’applicabilité expérimentale de nos idées dans des expériences d’optique quantique. Le thème principal de cette thèse est la formulation d’un cadre pour le traitement quantique de l’information dans l’espace des phases grâce aux variables modulaires. L’usage des variables modulaires permet d’encoder des états logique dans des espaces de Hilbert de dimension infinie et de définir des opérations qui permettent de les manipuler. En particulier, nous considérons des protocoles qui impliquent des mesures de variables modulaires qui permettent la lecture d’information discrète codée dans des variables continues. Grâce à ce formalisme, nous montrons comment il est possible de réaliser des tests des propriétés fondamentales de la mécanique quantique comme l’intrication, la non-localité ou la contextualité dans des espaces de Hilbert de dimensions finie ou infinie. Ensuite, nous discutons pourquoi les degrés de liberté transverse des photons sont des candidats naturels pour l’implémentation expérimentale des variables modulaires. À cet effet, nous démontrons comment il est possible d’utiliser l’effet Talbot - un effet d’interférence de champ proche - afin d’encoder de l’information discrète dans la distribution spatiales des photons. Finalement, nous montrons pour la première fois comment produire des photons intriqués de dimension arbitraire de manière déterministe en utilisant la conversion paramétrique et des éléments d’optique linéaire. / Quantum information can be processed in two fundamentally different ways, using either discrete- or continuous-variable implementations. In this thesis we study theoretically how to implement discrete quantum information protocols in physical objects characterized by continuous variables. In order to do so we use modular variables as a helpful tool to reveal discrete structures in continuous-variable states, operations and observables. The present work is strongly guided by the experimental applicability of our ideas in quantum optics experiments, with a particular focus on the transverse degrees of freedom of single photons. One of the main themes of this thesis is the formulation of a framework for quantum information processing in phase-space based on the use of modular variables. The latter permit us to introduce logical states and operations allowing to manipulate discrete quantum information encoded in infinite dimensional Hilbert spaces. In particular, we consider protocols that involve measurements of judiciously chosen logical observables enabling the readout of the encoded discrete quantum information. Based on this framework we show how to perform tests of fundamental properties of quantum mechanics, such as entanglement, Bell nonlocality and contextuality, in Hilbert spaces of various dimensions. Further on, we discuss the transverse degrees of freedom of single photons as a natural platform to manipulate and measure modular variables. In particular, we demonstrate how to process discrete quantum information encoded in the spatial distribution of single photons via the optical Talbot effect - a near-field interference effect. Finally, we show for the first time how to produce deterministically d-dimensional entangled photon pairs using spontaneous parametric down-conversion and linear optical elements only.

La mécanique quantique présente des propriétés étonnantes qui n'ont pas d'équivalent en physique classique. Ces propriétés sont au cœur des applications possibles de la mécanique quantique. Le thème principal de cette thèse est l'étude de deux des propriétés fondamentales de la mécanique quantique: la non-localité et la contextualité. Dans ce cadre, nous poursuivrons deux objectifs: premièrement, nous étudierons comment certains résultats obtenus pour les systèmes discrets peuvent être étendus aux systèmes décrits par des variables continues; deuxièmement nous étudierons comment il est possible de tester ces deux propriétés dans les systèmes quantiques décrits par des variables continues.Dans une première partie, nous étudions l'ensemble des distributions de probabilités locales et ``no-signaling'', c'est à dire qui ne permettent pas de transmettre d'information. Nous commençons par traduire le problème en terme de contraintes sur des espaces de mesures de probabilité. Nous introduisons ensuite un ensemble de mesures de probabilité qui sont les analogues en variables continues des probabilités découvertes par Popescu et Rohrlich dans le cas discret. Enfin, nous caractérisons l'ensemble des mesures de probabilité ``no-signaling''. Plus précisément, nous montrons que les mesures introduites sont des points extrémaux de l'ensemble des mesures de probabilité ``no-signaling'' et que leur enveloppe convexe est dense dans l'ensemble des mesures de probabilité ``no-signaling''. Dans une seconde partie nous nous intéressons à une preuve de la contextualité de la mécanique quantique dans une formulation qui ne dépend pas de l'état. Plus particulièrement, concernant l'inégalité de non-contextualité de Peres-Mermin, nous montrons qu'il est possible de la généraliser pour des observables définies sur des espaces de Hilbert de dimension arbitraire, voire infinie. Cette généralisation nous permet d'identifier les propriétés communes des observables qui conduisent à une violation maximale de l'inégalité de Peres-Mermin.En dernier lieu, nous nous intéressons à des états intriqués du champ électromagnétique de deux cavités. Ces états sont non-locaux et violent une inégalité de Bell formée de mesures de la parité déplacée. Nous étudions comment ces états peuvent être préparés et mesurés expérimentalement. Enfin, nous analysons l'effet des imperfections expérimentales et des pertes / Quantum mechanics has many intriguing properties that have no-classical analogs. These properties are at the heart of many quantum information protocols which offer the possibility to outperform their classical counterparts. This thesis is devoted to an investigation of two of the fundamental properties of quantum mechanics: non-locality and contextuality. The goal of this thesis is twofold. Firstly we will study how known results for discrete systems can be extended to continuous variables systems. Secondly, we will investigate how these properties can be tested in quantum systems characterized by continuous variables.Our work starts with an investigation of the set of local and no-signaling probability distributions. We develop a formalism for generic no-signaling black-box measurement devices with continuous outputs in terms of probability measures. We introduce the continuous-variable version of the famous Popescu-Rohrlich boxes and show that they violate the Tsirelson bound of an adequate continuous-variable Bell inequality. Finally, we perform a characterization of the geometry of the set of continuous-variable no-signaling correlations. More precisely, we show that the convex hull of those boxes is dense in the no-signaling set.We then study the contextuality of Quantum Mechanics in a state independent formulation. In particular, we study the Peres-Mermin state independent non-contextuality inequality, and show how it is possible to generalize the Peres-Mermin inequality to scenarios involving observables with an arbitrary number of outcomes. Specifically, we identify general conditions on the spectral decomposition of observables demonstrating state independent contextuality of quantum mechanics in this scenario.Lastly, we explore the non-local properties of entangled cat states, made of superpositions of coherent states stored in two spatially separated cavities. We show that even when taking into account the experimental imperfections such as the losses, a violation of local-realism is still possible, in the form of a violation of an appropriate Bell inequality

Researchers and therapists have given increasing attention and recognition to the cognitive components of marital distress. Numerous investigators have attempted to identify and operationalize key cognitive variables that are related to marital satisfaction. In doing so, researchers have looked at the differences between distressed and nondistressed couples in relation to certain categories of cognitive variables, hoping to demonstrate that a significant relationship exists between certain types of cognition and marital satisfaction. Although investigators agree that certain categories of cognition are directly related to marital satisfaction, there is no clear consensus on the degree of influence that these cognitive variables have on marital satisfaction and to what extent these variables are interrelated. The present study examined the relationship between marital satisfaction and four categories of cognition: casual attributions, expectancies, standards, and assumptions. Correlation analyses showed little if any multicolinearity between the independent variables. Stepwise regression analyses failed to yield a statistically significant model for predicting marital satisfaction using strictly these four independent variables. Although previous studies have demonstrated a relationship between scores on assessment measures for these four independent variables and marital satisfaction, the current sample did not follow this pattern.

The purpose of this study was to determine the reasons why students did not enroll at Utah State in the fall quarter of 1978 when they had listed the university as their first choice among institutions to attend. An equally important purpose was to determine whether or not there were differences in the personal characteristics of the enrolled and nonenrolled groups. Both students who entered U.S.U. in the fall quarter of 1978 and those who failed at that time to enroll served as samples for the study. A random sample of 150 students per group, 300 students altogether, was employed toward a determination of the specific reasons why students did not enroll. Both enrolled and nonenrolled students were mailed an identical questionnaire requesting reasons for enrollment or nonenrollment, depending on the student's circumstance. A third purpose was to use the results to develop recommendations which may help increase the percentage of applicants who become U.S.U. students. This study discovered differences between students enrolled at Utah State University and those not enrolled with respect to factors which might have influenced their decision to attend/not attend Utah State University. Differences between the two groups were found for the variables "printed materials and letters from U.S.U.", "campus visit", "major field of study", "social environment", "rank in graduating class" and "item influencing most their decision to attend/not attend U.S.U.". Differences between the two groups were found, also for the variables "finances", "recommendations", and "proximity to home". Various suggestions with respect to Utah State's recruitment and enrollment policies have been offered. It would appear to be in Utah State's best interest to have prospective students visit the U.S.U. campus as well as have the student's parents involved in the college decision-making process. It is recommended that prospective U.S.U. students be informed of financial aid applications and procedures as well as hear the recommendations of individuals who have had previous contact with Utah State University. It is suggested that the housing office of U.S.U. develop pamphlets, brochures, and other such information to be distributed to prospective students who will be living away from home when attending college.

Tesis para optar al grado de Magíster en Ciencias de la Ingeniería, Mención Matemáticas Aplicadas / Memoria para optar al título de Ingeniero Civil Matemático / En el clásico problema de tiempo de parada óptimo conocido como Desigualdad del profeta realizaciones de variables positivas e independientes son descubiertas secuencialmente. Una jugadora que conoce las distribuciones, pero no puede ver en el futuro, debe decidir cuándo parar y tomar la última variable revelada. Su objetivo es maximizar la esperanza de lo obtenido y su rendimiento está dado por el peor caso del cociente entre la esperanza de que obtiene y la esperanza de lo que obtendría un profeta (que puede ver en el futuro y así siempre elegir el máximo). En los setenta, Krengel y Sucheston, y Garling, [16] determinaron que el rendimiento de una jugadora puede ser una constante y que 1/2 es la mejor constante. En la última década, la desigualdad del profeta ha resurgido como un problema importante dada su conexión con "Posted Price Mechanisms", una teoría usada en ventas en línea. Una variante de particular interés es "Prophet Secretary", donde la única diferencia es que las relaciones son descubiertas en orden aleatorio. Para esta variante, varios algoritmos logran un rendimiento de 1 − 1/e ≈ 0.63 y recientemente Azar et al. [2] mejoraron este resultado. En cuanto a cotas superiores, se sabe que una jugadora no puede hacerlo mejor que 0.745, en el límite sobre el tamaño de la instancia. En esta tesis se deriva una forma de analizar estrategias que dependen sólo del tiempo: dada una instancia, se calcula una secuencia decreciente de exigencias que son usadas para decidir si parar o no. La jugadora tomará el primer valor que supere la exigencia correspondiente al momento en que fue descubierta. Específicamente, se considera una clase robusta de estrategias que denominamos "blind strategies". Constituyen una generalización de fijar una sola exigencia para todo el proceso y consisten en fijar una función, independiente de la instancia, que determina cómo calcular las exigencias una vez la instancia es conocida. El resultado principal es que la jugadora logra un rendimiento de al menos 0.669, superando el estado del arte (Azar et al. [2]) tanto para "Prophet Secretary" como para la variante en la que la jugadora tiene la libertad de escoger el orden en que descubre las variables (Beyhaghi et al [3]). El análisis se reduce a estudiar la distribución del tiempo de parada inducido por estas estrategias, a través de la teoría de Schur-convexidad. También, se demuestra que este tipo de estrategias no pueden lograr más que 0.675, a través de calcular el rendimiento óptimo de la jugadora contra dos instancias particulares, resolviendo un problema de control óptimo. Finalmente, se demuestra que el conjunto más amplio de estrategias no adaptativas no pueden lograr más de √3 − 1 ≈ 0.73, cota que también mejora el estado del arte en cotas superiores para estrategias simples (Azar et al [2]). Se considera una estrategia como no adaptativa si al decisión de parar depende del valor, la identidad y el tiempo en que fue descubierta la variable, pero no toma en cuenta la identidad de las variables anteriores. / CONICYT-Chile, ECOS-CONICYT, Google y CMM - Conicyt PIA AFB170001

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