<p>Longitudinal twin data provide important information for exploring sources of variation in human traits. In statistical models for twin data, unobserved genetic and environmental factors influencing the trait are represented by latent variables. In this way, trait variation can be decomposed into genetic and environmental components. With repeated measurements on twins, latent variables can be used to describe individual trajectories, and the genetic and environmental variance components are assessed as functions of age. This thesis contributes to statistical methodology for analysing longitudinal twin data by (i) exploring the use of random change point models for modelling variance as a function of age, (ii) assessing how nonresponse in twin studies may affect estimates of genetic and environmental influences, and (iii) providing a method for hypothesis testing of genetic and environmental variance components. The random change point model, in contrast to linear and quadratic random effects models, is shown to be very flexible in capturing variability as a function of age. Approximate maximum likelihood inference through first-order linearization of the random change point model is contrasted with Bayesian inference based on Markov chain Monte Carlo simulation. In a set of simulations based on a twin model for informative nonresponse, it is demonstrated how the effect of nonresponse on estimates of genetic and environmental variance components depends on the underlying nonresponse mechanism. This thesis also reveals that the standard procedure for testing variance components is inadequate, since the null hypothesis places the variance components on the boundary of the parameter space. The asymptotic distribution of the likelihood ratio statistic for testing variance components in classical twin models is derived, resulting in a mixture of chi-square distributions. Statistical methodology is illustrated with applications to empirical data on cognitive function from a longitudinal twin study of aging. </p>

Longitudinal twin data provide important information for exploring sources of variation in human traits. In statistical models for twin data, unobserved genetic and environmental factors influencing the trait are represented by latent variables. In this way, trait variation can be decomposed into genetic and environmental components. With repeated measurements on twins, latent variables can be used to describe individual trajectories, and the genetic and environmental variance components are assessed as functions of age. This thesis contributes to statistical methodology for analysing longitudinal twin data by (i) exploring the use of random change point models for modelling variance as a function of age, (ii) assessing how nonresponse in twin studies may affect estimates of genetic and environmental influences, and (iii) providing a method for hypothesis testing of genetic and environmental variance components. The random change point model, in contrast to linear and quadratic random effects models, is shown to be very flexible in capturing variability as a function of age. Approximate maximum likelihood inference through first-order linearization of the random change point model is contrasted with Bayesian inference based on Markov chain Monte Carlo simulation. In a set of simulations based on a twin model for informative nonresponse, it is demonstrated how the effect of nonresponse on estimates of genetic and environmental variance components depends on the underlying nonresponse mechanism. This thesis also reveals that the standard procedure for testing variance components is inadequate, since the null hypothesis places the variance components on the boundary of the parameter space. The asymptotic distribution of the likelihood ratio statistic for testing variance components in classical twin models is derived, resulting in a mixture of chi-square distributions. Statistical methodology is illustrated with applications to empirical data on cognitive function from a longitudinal twin study of aging.

En la tesi s'aborda el problema de l'homogeneïtat d'estil en el Tirant lo Blanc mitjançant l'ús de l'estilometria. Les hipòtesis al voltant de l'autoria del Tirant lo Blanc van des de l'autoria única de Joanot Martorell a la intervenció d'un segon autor, be a l'última part de la novel·la o be al llarg de tota ella, passant per altres teories més heterodoxes. A la primera part de la tesi es fa un breu repàs dels problemes que aborda l'estilometria i d'algunes eines estadístiques útils a l'hora de fer un estudi quantitatiu de l'estil literari, es resumeix la qüestió de l'autoria del Tirant lo Blanc, i es descriu la base de dades que s'ha construït per la quantificació de l'estil en el Tirant. Per atacar el problema, hem començat adaptant tècniques d'anàlisi descriptiva de dades, com els gràfics de control i l'anàlisi de correspondències. Per explotar la base de dades, proposem un mètode pràctic per estimar un o més d'un punt de canvi en seqüències de normals, de binomials i de multinomials. El mètode es basa en l'ajust de models i troba els estimadors màxim versemblants del(s) punt(s) de canvi. També hem utilitzat un mètode cluster basat en l'ajust de models per a dades politòmiques, per a agrupar les files d'una taula de contingència. Vam començar l'estudi fent un estudi comparatiu de 12 maneres diferents de mesurar la riquesa i diversitat de vocabulari. Pel que fa a les unitats lexicomètriques la llargada de paraula i l'ús de paraules freqüents i lliures del context ens han sigut molt útils per a l'estimació del punt de canvi i l'atribució d'estil als capítols. L'ús de lletres, tot i ser menys útil, serveix per a reforçar l'evidència del que trobem amb les unitats abans esmentades. La llargada de frase i la de capítol no ens ha sigut útils per a determinar una frontera d'estil en el Tirant.Per tot el que hem anat trobant estem convençuts que hi ha un canvi sobtat en l'estil entre els capítols 371 i 382, que difícilment pot ser atribuïble a l'argument. També hem trobat que després del punt de canvi conviuen capítols amb els dos estils, el que probablement reforça la teoria de que un segon autor va afegir capítols sobre un original pràcticament acabat. De totes maneres, no ens pertoca a nosaltres descobrir que el canvi d'estil no pugui ser degut a altres raons. / En la tesis se aborda el problema de la homogeneidad de estilo en el Tirant lo Blanc mediante el uso de la estilometría. Las hipótesis sobre la autoría del Tirant lo Blanc van desde la autoría única de Joanot Martorell a la intervención de un segundo autor, bien en la última parte de la novela o bien a lo largo de toda ella, pasando por otras teorías más heterodoxas. En la primera parte de la tesis se hace un breve repaso de los problemas que aborda la estilometría i de algunas herramienta estadísticas útiles para el estudio cuantitativo del estilo literario, se resume la cuestión de la autoría del Tirant lo Blanc, y se describe la base de datos que s ha construido para la ciantificación del estilo en el Tirant. Para atacar el problema, hemos empezado adaptando técnicas de análisis descriptivo de datos, como los gráficos de control y el análisis de correspondencias. Para explotar la base de datos, proponemos un método práctico para estimar uno o más de un punto de cambio en secuencias de normales, de binomiales y de multinomiales. El método se basa en el ajuste de modelos y halla los estimadores máximo verosímiles del (de los) punto(s) de cambio. También hemo utilizado un método cluster basado en el ajuste de modelos para a datos politómicos, para agrupar las filas de una tabla de contingencia. Empezamos el estudio realizando un estudio comparativo de 12 formas diferentes de medir la riqueza y diversidad de vocabulario. Las unidades lexicométricas como la longitud de palabra y el uso de palabras frecuentes y libres del contexto nos han sido muy útiles para la estimación del punto de cambio y la atribución de estilo a los capítulos. El uso de letras, a pesar de ser menos útil, sirve para reforzar la evidencia de lo que hallamos con las unidades antes citadas. La longitud de frase y la de capítulo no nos han sido útiles para a determinar una frontera de estilo en el Tirant.Por todos los resultados que hemos ido obteniendo, estamos convencidos que hay un cambio repentino en el estilo entre los capítulos 371 y 382, que difícilmente puede ser atribuible al argumento. También hemos observado que después del punto de cambio conviven capítulos con los dos estilos, lo que probablemente refuerza la teoría de que un segundo autor añadió capítulos sobre un original prácticamente acabado. De todas maneras, no es nuestra misión descubrir que el cambio de estilo no pueda ser debido a otras razones. / This Ph.D. Thesis tackles the problem of the homogeneity of style in Tirant lo Blanc, using the statistical analysis of stylistic features that are measurable but rarely consciously controlled by the author. The goal is to determine whether the style in the book is homogeneous and, if it is not, to find stylistic boundaries. Tirant lo Blanc is the main work in Catalan literature, a chivalry book hailed to be 'the best book of its kind in the world' by Cervantes in Don Quixote, and is considered to be the first modern novel in Europe. There has been an intense and long lasting debate around its authorship originating from conflicting information given in its first edition; while the dedicatory letter states that Joanot Martorell takes sole responsibility for writing the book, the colophon states that the last quarter of the book was written by Martí Joan de Galba, after the death of Martorell. Neither of the two candidate authors left any text comparable to the one under study, and therefore one can not use discriminant analysis to help classify the chapters in the book by author. The majority opinion among medievalists leans towards the single-authorship hypothesis, even though there is a rather strong dissenting minority. In the first part of the thesis we summarize some useful statistical techniques for the quantitative analysis of literary style, we describe the problems that stylometry deals with and we give the state-of-the-art of the authorship attribution problem in Tirant lo Blanc. The data base built by the quantification of style is described as well. The analysis is started by the use of graphical, Statistical Process Control and Correspondence Analysis techniques. In order to obtain maximum likelihood estimates of one or more than one change points in either normal, binomial or multinomial sequences, we propose a practical method based on the fitting of Generalized Linear Models. A cluster method for the rows of a contingency table, based on the fitting of models, is proposed too. We analyze the evolution of the diversity of the vocabulary used in the book through twelve different diversity indices. Following the lead of the extensive stylometry literature, we use word length, and the use of function words to estimate the change point and the attribution of style to the 489 chapters of the book. The use of letters, in spite of being less useful, reinforces the evidences found with the units previously cited. The sentence length and the chapter length weren't useful to determine a style boundary in Tirant The statistical analysis consistently detects a change in style somewhere between chapters 371 and 382, even though a few chapters at the end have a style similar to the ones before that boundary. It is important to remark that even though the statistical analysis supports the existence of two authors, it is not up to us to exclude the possibility that the stylistic boundary found could be explained otherwise.

Wavelet methods possess versatile properties for statistical applications. We would like to explore the advantages of using wavelets in the analyses in two different research areas. First of all, we develop an integrated tool for online detection of network anomalies. We consider statistical change point detection algorithms, for both local changes in the variance and for jumps detection, and propose modified versions of these algorithms based on moving window techniques. We investigate performances on simulated data and on network traffic data with several superimposed attacks. All detection methods are based on wavelet packets transformations. We also propose a Bayesian model for the analysis of high-throughput data where the outcome of interest has a natural ordering. The method provides a unified approach for identifying relevant markers and predicting class memberships. This is accomplished by building a stochastic search variable selection method into an ordinal model. We apply the methodology to the analysis of proteomic studies in prostate cancer. We explore wavelet-based techniques to remove noise from the protein mass spectra. The goal is to identify protein markers associated with prostate-specific antigen (PSA) level, an ordinal diagnostic measure currently used to stratify patients into different risk groups.

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In recent years, trade activity in stock markets has increased substantially. This is mainly attributed to the development of powerful computers and intranets connecting traders to markets across the globe. The trades have to be carried out almost instantaneously and the systems in place that handle trades are burdened with millions of transactions a day, several thousand a minute. With increasing transactions the time to execute a single trade increases, and this can be seen as an impact on the performance. There is a need to model the performance of these systems and provide forecasts to give a heads up on when a system is expected to be overwhelmed by transactions. This was done in this study, in cooperation with Cinnober Financial Technologies, a firm which provides trading solutions to stock markets. To ensure that the models developed weren‟t biased, the dataset was cleansed, i.e. operational and other transactions were removed, and only valid trade transactions remained. For this purpose, a descriptive analysis of time series along with change point detection and LOESS regression were used. State space model with Kalman Filtering was further used to develop a time varying coefficient model for the performance, and this model was applied to make forecasts. Wavelets were also used to produce forecasts, and besides this high pass filters were used to identify low performance regions. The State space model performed very well to capture the overall trend in performance and produced reliable forecasts. This can be ascribed to the property of Kalman Filter to handle noisy data well. Wavelets on the other hand didn‟t produce reliable forecasts but were more efficient in detecting regions of low performance.

We provide a flexible means of estimating time-varying parameter models in a Bayesian framework. By specifying the state innovations to be characterized trough a threshold process that is driven by the absolute size of parameter changes, our model detects at each point in time whether a given regression coefficient is constant or time-varying. Moreover, our framework accounts for model uncertainty in a data-based fashion through Bayesian shrinkage priors on the initial values of the states. In a simulation, we show that our model reliably identifies regime shifts in cases where the data generating processes display high, moderate, and low numbers of movements in the regression parameters. Finally, we illustrate the merits of our approach by means of two applications. In the first application we forecast the US equity premium and in the second application we investigate the macroeconomic effects of a US monetary policy shock. / Series: Department of Economics Working Paper Series

This thesis discusses the changes in parameters of linear models and methods of their detection. It begins with a short introduction of the two basic types of change point detection procedures and bootstrap algorithms developed specifically to deal with dependent data. In the following chapter we focus on the location model - the simplest example of a linear model with a change in parameters. On this model we will illustrate a way of long-run variance estimation and implementation of selected bootstrap procedures. In the last chapter we show how to extend the applied methods to linear models with a change in parameters. We will compare the performance of change point tests based on asymptotic and bootstrap critical values through simulation studies in both our considered methods. The performance of selected long-run variance estimator will also be examined both for situations when the change in parameters occurs and when it does not. 1

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This thesis addresses the problem of detecting changes in the activity of a distant gas source from the response of an array of metal oxide (MOX) gas sensors deployed in an Open Sampling System (OSS). Changes can occur due to gas source activity such as a sudden alteration in concentration or due to exposure to a different compound. Applications such as gas-leak detection in mines or large-scale pollution monitoring can benefit from reliable change detection algorithms, especially where it is impractical to continuously store or transfer sensor readings, or where reliable calibration is difficult to achieve. Here, it is desirable to detect a change point indicating a significant event, e.g. presence of gas or a sudden change in concentration. The main challenges are turbulent dispersion of gas and the slow response and recovery times of MOX sensors. Due to these challenges, the gas sensor response exhibits fluctuations that interfere with the changes of interest. The contributions of this thesis are centred on developing change detection methods using MOX sensor responses. First, we apply the Generalized Likelihood Ratio algorithm (GLR), a commonly used method that does not make any a priori assumption about change events. Next, we propose TREFEX, a novel change point detection algorithm, which models the response of MOX sensors as a piecewise exponential signal and considers the junctions between consecutive exponentials as change points. We also propose the rTREFEX algorithm as an extension of TREFEX. The core idea behind rTREFEX is an attempt to improve the fitted exponentials of TREFEX by minimizing the number of exponentials even further. GLR, TREFEX and rTREFEX are evaluated for various MOX sensors and gas emission profiles. A sensor selection algorithm is then introduced and the change detection algorithms are evaluated with the selected sensor subsets. A comparison between the three proposed algorithms shows clearly superior performance of rTREFEX both in detection performance and in estimating the change time. Further, rTREFEX is evaluated in real-world experiments where data is gathered by a mobile robot. Finally, a gas dispersion simulation was developed which integrates OpenFOAM flow simulation and a filament-based gas propagation model to simulate gas dispersion for compressible flows with a realistic turbulence model.