On the relationship between the Method of Least Squares and Gram-Schmidt orthogonalization

The method of Least Squares is due to Carl Friedrich Gauss. The Gram-Schmidt orthogonalization method is of much younger date. A method for solving Least Squares Problems is developed which automatically results in the appearance of the Gram-Schmidt orthogonalizers. Given these orthogonalizers an induction-proof is available for solving Least Squares Problems.

Hierarchical Mixtures of Experts and the EM Algorithm

We present a tree-structured architecture for supervised learning. The statistical model underlying the architecture is a hierarchical mixture model in which both the mixture coefficients and the mixture components are generalized linear models (GLIM's). Learning is treated as a maximum likelihood problem; in particular, we present an Expectation-Maximization (EM) algorithm for adjusting the parameters of the architecture. We also develop an on-line learning algorithm in which the parameters are updated incrementally. Comparative simulation results are presented in the robot dynamics domain.

Alternative ways to estimate change points in multinomial sequences. An application to an authorship attribution problem

The statistical analysis of literary style is the part of stylometry that compares measurable characteristics in a text that are rarely controlled by the author, with those in other texts. When the goal is to settle authorship questions, these characteristics should relate to the author’s style and not to the genre, epoch or editor, and they should be such that their variation between authors is larger than the variation within comparable texts from the same author. For an overview of the literature on stylometry and some of the techniques involved, see for example Mosteller and Wallace (1964, 82), Herdan (1964), Morton (1978), Holmes (1985), Oakes (1998) or Lebart, Salem and Berry (1998). Tirant lo Blanc, a chivalry book, is the main work in catalan literature and it was hailed to be “the best book of its kind in the world” by Cervantes in Don Quixote. Considered by writters like Vargas Llosa or Damaso Alonso to be the first modern novel in Europe, it has been translated several times into Spanish, Italian and French, with modern English translations by Rosenthal (1996) and La Fontaine (1993). The main body of this book was written between 1460 and 1465, but it was not printed until 1490. There is an intense and long lasting debate around its authorship sprouting from its first edition, where its introduction states that the whole book is the work of Martorell (1413?-1468), while at the end it is stated that the last one fourth of the book is by Galba (?-1490), after the death of Martorell. Some of the authors that support the theory of single authorship are Riquer (1990), Chiner (1993) and Badia (1993), while some of those supporting the double authorship are Riquer (1947), Coromines (1956) and Ferrando (1995). For an overview of this debate, see Riquer (1990). Neither of the two candidate authors left any text comparable to the one under study, and therefore discriminant analysis can not be used to help classify chapters by author. By using sample texts encompassing about ten percent of the book, and looking at word length and at the use of 44 conjunctions, prepositions and articles, Ginebra and Cabos (1998) detect heterogeneities that might indicate the existence of two authors. By analyzing the diversity of the vocabulary, Riba and Ginebra (2000) estimates that stylistic boundary to be near chapter 383. Following the lead of the extensive literature, this paper looks into word length, the use of the most frequent words and into the use of vowels in each chapter of the book. Given that the features selected are categorical, that leads to three contingency tables of ordered rows and therefore to three sequences of multinomial observations. Section 2 explores these sequences graphically, observing a clear shift in their distribution. Section 3 describes the problem of the estimation of a suden change-point in those sequences, in the following sections we propose various ways to estimate change-points in multinomial sequences; the method in section 4 involves fitting models for polytomous data, the one in Section 5 fits gamma models onto the sequence of Chi-square distances between each row profiles and the average profile, the one in Section 6 fits models onto the sequence of values taken by the first component of the correspondence analysis as well as onto sequences of other summary measures like the average word length. In Section 7 we fit models onto the marginal binomial sequences to identify the features that distinguish the chapters before and after that boundary. Most methods rely heavily on the use of generalized linear models

Mixing compositions and other scales

Theory of compositional data analysis is often focused on the composition only. However in practical applications we often treat a composition together with covariables with some other scale. This contribution systematically gathers and develop statistical tools for this situation. For instance, for the graphical display of the dependence of a composition with a categorical variable, a colored set of ternary diagrams might be a good idea for a first look at the data, but it will fast hide important aspects if the composition has many parts, or it takes extreme values. On the other hand colored scatterplots of ilr components could not be very instructive for the analyst, if the conventional, black-box ilr is used. Thinking on terms of the Euclidean structure of the simplex, we suggest to set up appropriate projections, which on one side show the compositional geometry and on the other side are still comprehensible by a non-expert analyst, readable for all locations and scales of the data. This is e.g. done by defining special balance displays with carefully- selected axes. Following this idea, we need to systematically ask how to display, explore, describe, and test the relation to complementary or explanatory data of categorical, real, ratio or again compositional scales. This contribution shows that it is sufficient to use some basic concepts and very few advanced tools from multivariate statistics (principal covariances, multivariate linear models, trellis or parallel plots, etc.) to build appropriate procedures for all these combinations of scales. This has some fundamental implications in their software implementation, and how might they be taught to analysts not already experts in multivariate analysis

Modeling of hybrid systems by piecewise decomposition

Piecewise linear models systems arise as mathematical models of systems in many practical applications, often from linearization for nonlinear systems. There are two main approaches of dealing with these systems according to their continuous or discrete-time aspects. We propose an approach which is based on the state transformation, more particularly the partition of the phase portrait in different regions where each subregion is modeled as a two-dimensional linear time invariant system. Then the Takagi-Sugeno model, which is a combination of local model is calculated. The simulation results show that the Alpha partition is well-suited for dealing with such a system

La educación secundaria y sus dos dimensiones, efectos del barrio y del colegio sobre los resultados saber 11.

Resumen: Este trabajo estudia los resultados en matemáticas y lenguaje de 32000 estudiantes en la prueba saber 11 del 2008, de la ciudad de Bogotá. Este análisis reconoce que los individuos se encuentran contenidos en barrios y colegios, pero no todos los individuos del mismo barrio asisten a la misma escuela y viceversa. Con el fin de modelar esta estructura de datos se utilizan varios modelos econométricos, incluyendo una regresión jerárquica multinivel de efectos cruzados. Nuestro objetivo central es identificar en qué medida y que condiciones del barrio y del colegio se correlacionan con los resultados educacionales de la población objetivo y cuáles características de los barrios y de los colegios están más asociadas al resultado en las pruebas. Usamos datos de la prueba saber 11, del censo de colegios c600, del censo poblacional del 2005 y de la policía metropolitana de Bogotá. Nuestras estimaciones muestran que tanto el barrio como el colegio están correlacionados con los resultados en las pruebas; pero el efecto del colegio parece ser mucho más fuerte que el del barrio. Las características del colegio que están más asociadas con el resultado en las pruebas son la educación de los profesores, la jornada, el valor de la pensión, y el contexto socio económico del colegio. Las características de los barrios más asociadas con el resultado en las pruebas son, la presencia de universitarios en la UPZ, un clúster de altos niveles de educación y nivel de crimen en el barrio que se correlaciona negativamente. Los resultados anteriores fueron hallados teniendo en cuenta controles familiares y personales.

Prevalencia de delirium en población adulta en cuidado intensivo.

Introducción: El delirium es un trastorno de conciencia de inicio agudo asociado a confusión o disfunción cognitiva, se puede presentar hasta en 42% de pacientes, de los cuales hasta el 80% ocurren en UCI. El delirium aumenta la estancia hospitalaria, el tiempo de ventilación mecánica y la morbimortalidad. Se pretendió evaluar la prevalencia de periodo de delirium en adultos que ingresaron a la UCI en un hospital de cuarto nivel durante 2012 y los factores asociados a su desarrollo. Metodología Se realizó un estudio transversal con corte analítico, se incluyeron pacientes hospitalizados en UCI médica y UCI quirúrgica. Se aplicó la escala de CAM-ICU y el Examen Mínimo del Estado Mental para evaluar el estado mental. Las asociaciones significativas se ajustaron con análisis multivariado. Resultados: Se incluyeron 110 pacientes, el promedio de estancia fue 5 días; la prevalencia de periodo de delirium fue de 19.9%, la mediana de edad fue 64.5 años. Se encontró una asociación estadísticamente significativa entre el delirium y la alteración cognitiva de base, depresión, administración de anticolinérgicos y sepsis (p< 0,05). Discusión Hasta la fecha este es el primer estudio en la institución. La asociación entre delirium en la UCI y sepsis, uso de anticolinérgicos, y alteración cognitiva de base son consistentes y comparables con factores de riesgo descritos en la literatura mundial.

Determinants of demand for antenatal care in Colombia

Even though antenatal care is universally regarded as important, determinants of demand for antenatal care have not been widely studied. Evidence concerning which and how socioeconomic conditions influence whether a pregnant woman attends or not at least one antenatal consultation or how these factors affect the absences to antenatal consultations is very limited. In order to generate this evidence, a two-stage analysis was performed with data from the Demographic and Health Survey carried out by Profamilia in Colombia during 2005. The first stage was run as a logit model showing the marginal effects on the probability of attending the first visit and an ordinary least squares model was performed for the second stage. It was found that mothers living in the pacific region as well as young mothers seem to have a lower probability of attending the first visit but these factors are not related to the number of absences to antenatal consultation once the first visit has been achieved. The effect of health insurance was surprising because of the differing effects that the health insurers showed. Some familiar and personal conditions such as willingness to have the last children and number of previous children, demonstrated to be important in the determination of demand. The effect of mother’s educational attainment was proved as important whereas the father’s educational achievement was not. This paper provides some elements for policy making in order to increase the demand inducement of antenatal care, as well as stimulating research on demand for specific issues on health.

Natural resource windfalls and efficiency of local government expenditures: evidence from Peru

We study the role of natural resource windfalls in explaining the efficiency of public expenditures. Using a rich dataset of expenditures and public good provision for 1,836 municipalities in Peru for period 2001-2010, we estimate a non-monotonic relationship between the efficiency of public good provision and the level of natural resource transfers. Local governments that were extremely favored by the boom of mineral prices were more efficient in using fiscal windfalls whereas those benefited with modest transfers were more inefficient. These results can be explained by the increase in political competition associated with the boom. However, the fact that increases in efficiency were related to reductions in public good provision casts doubts about the beneficial effects of political competition in promoting efficiency.

Estudio comparativo sobre la influencia del adulto en la actividad cognitiva del niño trisómico-niño normal entre 11 meses a 18 meses.

Conocer las bases y organización de la estructura intelectual defectuosa, comparativamente con la normal. Conocer cúal es la incidencia del adulto en dicha construcción, acentuando su papel en la elaboración de la deficiencia. 3 bebés normales observados desde los 8 meses hasta los 18 meses y 3 bebés con síndrome de Down, observados desde la edad madurativa equivalente a los 11 meses. Plantea un marco teórico basado en un punto de vista constructivista e interaccionista centrado en el eje inteligencia-acción-interacción. El marco explicativo respecto al desarrollo defectuoso es el de la teoría de la deficiencia, y el del desarrollo normal se basa en la teoría piagetiana. Plantea dos hipótesis de trabajo. Elige una muestra compuesta por seis casos de manera no aleatoria. Obtiene los datos a partir de la observación sistematizada y longitudinal de los dos grupos de la muestra (normales y trisómicos). Registra su actividad espontánea resultante de jugar con material cerrado, durante 10 minutos y en presencia de dos adultos. Realiza un análisis de datos cualitativo y cuantitativo a tres niveles : intra-sujeto, intra-grupo e inter-grupo. Observación sistemática (funcional, natural, longitudinal, comparativa). Material de juego de tipo no figurativo, favorecedor de actividades lógicas. Análisis cualitativo: codificación y categorización del material y acciones. Análisis cuantitativo: coeficiente de consistencia intra-observador de Knippendorf. Análisis log-linear mediante el paquete estadístico BMDP/4F. Concordancias entre los dos grupos: necesidad del feed-back acción niño-modelo, adulto- respuesta niño. Necesidad de la adecuación del modelo adulto a la actividad del niño. Necesidad de la intersubjetividad adulto-niño. Diferencias entre grupos respecto a: la generación del proyecto de acción y la significación conferida así como a la intersubjetividad, mostrando mayor dificultad el grupo trisómico. La regulación mutua, necesaria pero difícilmente observado en el grupo de trisómicos. La intervención del adulto en la actividad cognitiva del niño es positiva o negativa en función de la existencia o no de un proyecto de acción infantil, significación compartida, intersubjetividad, adecuación mutua adulto-niño y el feed-back entre ellos.

Influencia de las variables contextuales en el rendimiento escolar de octavo de EGB.

Estudiar la influencia de las variables contextuales en el rendimiento académico y, más especificamente, aquellas que ejercen en los contextos académicos, social, geográfico, etc. sobre el rendimiento escolar. 5380 alumnos de octavo de EGB. Pruebas psicopedagógicas y cuestionarios. Tablas de contingencia muldimensional, análisis log linear, análisis factorial, porcentajes y análisis de significación estadística. Esta investigación parte de la formulación de cuatro hipótesis referidas al grado de asociación existente entre variables que constituyen un grupo de variables dependientes (variables de rendimiento) y el grupo de las independientes (variables contextuales), así como lo que se establece entre ellas en el ciclo inicial, con el fin de cubrir la carencia de instrumentos de análisis a la vez que buscar un diseño que integre todas las dimensiones textuales como un discurso homogéneo y secuenciado. Una vez elaborado el instrumento se realiza una aplicación en una muestra de textos para ponerlo a prueba y demostrar en la práctica su funcionamiento y procedimiento de aplicación. Los datos fueron recogidos aplicando pruebas psicopedagógicas aplicadas por el CIDE. La media del rendimiento escolar viene determinada por las calificaciones emitidas por el profesor y una nota global, media de todas ellas, junto a los resultados de las pruebas objetivas. Como conclusión se establece las siguientes relaciones entre variables: a) las variables contextuales establecen relaciones significativas con las variables de rendimiento estudiadas, y estas relaciones son más fijas y permanentes, sino que están determinadas por variables moduladoras medias del rendimiento; b) las variables independientes que ejercen una mayor incidencia en las dependientes son aquellas que aluden a aspectos estructurales (estratificación social), institucionales (tipo de centro) y académicas (repetición del curso y asistencia preescolar); c) los resultados obtenidos en las calificaciones parecen establecer relaciones menos sensibles al influjo de las variables contextuales que a las pruebas objetivas. Fecha finalización tomada del Código del Documento.

Internal test sets studies in a group of antimalarials

Topological indices have been applied to build QSAR models for a set of 20 antimalarial cyclic peroxy cetals. In order to evaluate the reliability of the proposed linear models leave-n-out and Internal Test Sets (ITS) approaches have been considered. The proposed procedure resulted in a robust and consensued prediction equation and here it is shown why it is superior to the employed standard cross-validation algorithms involving multilinear regression models

Modelling, control and supervision for a class of hybrid systems

The aim of this thesis is to narrow the gap between two different control techniques: the continuous control and the discrete event control techniques DES. This gap can be reduced by the study of Hybrid systems, and by interpreting as Hybrid systems the majority of large-scale systems. In particular, when looking deeply into a process, it is often possible to identify interaction between discrete and continuous signals. Hybrid systems are systems that have both continuous, and discrete signals. Continuous signals are generally supposed continuous and differentiable in time, since discrete signals are neither continuous nor differentiable in time due to their abrupt changes in time. Continuous signals often represent the measure of natural physical magnitudes such as temperature, pressure etc. The discrete signals are normally artificial signals, operated by human artefacts as current, voltage, light etc. Typical processes modelled as Hybrid systems are production systems, chemical process, or continuos production when time and continuous measures interacts with the transport, and stock inventory system. Complex systems as manufacturing lines are hybrid in a global sense. They can be decomposed into several subsystems, and their links. Another motivation for the study of Hybrid systems is the tools developed by other research domains. These tools benefit from the use of temporal logic for the analysis of several properties of Hybrid systems model, and use it to design systems and controllers, which satisfies physical or imposed restrictions. This thesis is focused in particular types of systems with discrete and continuous signals in interaction. That can be modelled hard non-linealities, such as hysteresis, jumps in the state, limit cycles, etc. and their possible non-deterministic future behaviour expressed by an interpretable model description. The Hybrid systems treated in this work are systems with several discrete states, always less than thirty states (it can arrive to NP hard problem), and continuous dynamics evolving with expression: with Ki ¡ Rn constant vectors or matrices for X components vector. In several states the continuous evolution can be several of them Ki = 0. In this formulation, the mathematics can express Time invariant linear system. By the use of this expression for a local part, the combination of several local linear models is possible to represent non-linear systems. And with the interaction with discrete events of the system the model can compose non-linear Hybrid systems. Especially multistage processes with high continuous dynamics are well represented by the proposed methodology. Sate vectors with more than two components, as third order models or higher is well approximated by the proposed approximation. Flexible belt transmission, chemical reactions with initial start-up and mobile robots with important friction are several physical systems, which profits from the benefits of proposed methodology (accuracy). The motivation of this thesis is to obtain a solution that can control and drive the Hybrid systems from the origin or starting point to the goal. How to obtain this solution, and which is the best solution in terms of one cost function subject to the physical restrictions and control actions is analysed. Hybrid systems that have several possible states, different ways to drive the system to the goal and different continuous control signals are problems that motivate this research. The requirements of the system on which we work is: a model that can represent the behaviour of the non-linear systems, and that possibilities the prediction of possible future behaviour for the model, in order to apply an supervisor which decides the optimal and secure action to drive the system toward the goal. Specific problems can be determined by the use of this kind of hybrid models are: - The unity of order. - Control the system along a reachable path. - Control the system in a safe path. - Optimise the cost function. - Modularity of control The proposed model solves the specified problems in the switching models problem, the initial condition calculus and the unity of the order models. Continuous and discrete phenomena are represented in Linear hybrid models, defined with defined eighth-tuple parameters to model different types of hybrid phenomena. Applying a transformation over the state vector : for LTI system we obtain from a two-dimensional SS a single parameter, alpha, which still maintains the dynamical information. Combining this parameter with the system output, a complete description of the system is obtained in a form of a graph in polar representation. Using Tagaki-Sugeno type III is a fuzzy model which include linear time invariant LTI models for each local model, the fuzzyfication of different LTI local model gives as a result a non-linear time invariant model. In our case the output and the alpha measure govern the membership function. Hybrid systems control is a huge task, the processes need to be guided from the Starting point to the desired End point, passing a through of different specific states and points in the trajectory. The system can be structured in different levels of abstraction and the control in three layers for the Hybrid systems from planning the process to produce the actions, these are the planning, the process and control layer. In this case the algorithms will be applied to robotics ¡V a domain where improvements are well accepted ¡V it is expected to find a simple repetitive processes for which the extra effort in complexity can be compensated by some cost reductions. It may be also interesting to implement some control optimisation to processes such as fuel injection, DC-DC converters etc. In order to apply the RW theory of discrete event systems on a Hybrid system, we must abstract the continuous signals and to project the events generated for these signals, to obtain new sets of observable and controllable events. Ramadge & Wonham¡¦s theory along with the TCT software give a Controllable Sublanguage of the legal language generated for a Discrete Event System (DES). Continuous abstraction transforms predicates over continuous variables into controllable or uncontrollable events, and modifies the set of uncontrollable, controllable observable and unobservable events. Continuous signals produce into the system virtual events, when this crosses the bound limits. If this event is deterministic, they can be projected. It is necessary to determine the controllability of this event, in order to assign this to the corresponding set, , controllable, uncontrollable, observable and unobservable set of events. Find optimal trajectories in order to minimise some cost function is the goal of the modelling procedure. Mathematical model for the system allows the user to apply mathematical techniques over this expression. These possibilities are, to minimise a specific cost function, to obtain optimal controllers and to approximate a specific trajectory. The combination of the Dynamic Programming with Bellman Principle of optimality, give us the procedure to solve the minimum time trajectory for Hybrid systems. The problem is greater when there exists interaction between adjacent states. In Hybrid systems the problem is to determine the partial set points to be applied at the local models. Optimal controller can be implemented in each local model in order to assure the minimisation of the local costs. The solution of this problem needs to give us the trajectory to follow the system. Trajectory marked by a set of set points to force the system to passing over them. Several ways are possible to drive the system from the Starting point Xi to the End point Xf. Different ways are interesting in: dynamic sense, minimum states, approximation at set points, etc. These ways need to be safe and viable and RchW. And only one of them must to be applied, normally the best, which minimises the proposed cost function. A Reachable Way, this means the controllable way and safe, will be evaluated in order to obtain which one minimises the cost function. Contribution of this work is a complete framework to work with the majority Hybrid systems, the procedures to model, control and supervise are defined and explained and its use is demonstrated. Also explained is the procedure to model the systems to be analysed for automatic verification. Great improvements were obtained by using this methodology in comparison to using other piecewise linear approximations. It is demonstrated in particular cases this methodology can provide best approximation. The most important contribution of this work, is the Alpha approximation for non-linear systems with high dynamics While this kind of process is not typical, but in this case the Alpha approximation is the best linear approximation to use, and give a compact representation.

Serial clustering of extratropical cyclones

The clustering in time (seriality) of extratropical cyclones is responsible for large cumulative insured losses in western Europe, though surprisingly little scientific attention has been given to this important property. This study investigates and quantifies the seriality of extratropical cyclones in the Northern Hemisphere using a point-process approach. A possible mechanism for serial clustering is the time-varying effect of the large-scale flow on individual cyclone tracks. Another mechanism is the generation by one parent cyclone of one or more offspring through secondary cyclogenesis. A long cyclone-track database was constructed for extended October March winters from 1950 to 2003 using 6-h analyses of 850-mb relative vorticity derived from the NCEP NCAR reanalysis. A dispersion statistic based on the varianceto- mean ratio of monthly cyclone counts was used as a measure of clustering. It reveals extensive regions of statistically significant clustering in the European exit region of the North Atlantic storm track and over the central North Pacific. Monthly cyclone counts were regressed on time-varying teleconnection indices with a log-linear Poisson model. Five independent teleconnection patterns were found to be significant factors over Europe: the North Atlantic Oscillation (NAO), the east Atlantic pattern, the Scandinavian pattern, the east Atlantic western Russian pattern, and the polar Eurasian pattern. The NAO alone is not sufficient for explaining the variability of cyclone counts in the North Atlantic region and western Europe. Rate dependence on time-varying teleconnection indices accounts for the variability in monthly cyclone counts, and a cluster process did not need to be invoked.

Stochastic modelling of rainfall from satellite data

Satellite-based rainfall monitoring is widely used for climatological studies because of its full global coverage but it is also of great importance for operational purposes especially in areas such as Africa where there is a lack of ground-based rainfall data. Satellite rainfall estimates have enormous potential benefits as input to hydrological and agricultural models because of their real time availability, low cost and full spatial coverage. One issue that needs to be addressed is the uncertainty on these estimates. This is particularly important in assessing the likely errors on the output from non-linear models (rainfall-runoff or crop yield) which make use of the rainfall estimates, aggregated over an area, as input. Correct assessment of the uncertainty on the rainfall is non-trivial as it must take account of • the difference in spatial support of the satellite information and independent data used for calibration • uncertainties on the independent calibration data • the non-Gaussian distribution of rainfall amount • the spatial intermittency of rainfall • the spatial correlation of the rainfall field This paper describes a method for estimating the uncertainty on satellite-based rainfall values taking account of these factors. The method involves firstly a stochastic calibration which completely describes the probability of rainfall occurrence and the pdf of rainfall amount for a given satellite value, and secondly the generation of ensemble of rainfall fields based on the stochastic calibration but with the correct spatial correlation structure within each ensemble member. This is achieved by the use of geostatistical sequential simulation. The ensemble generated in this way may be used to estimate uncertainty at larger spatial scales. A case study of daily rainfall monitoring in the Gambia, west Africa for the purpose of crop yield forecasting is presented to illustrate the method.