No description available.

BACKGROUND - Bipolar disorder has been postulated as an explanation for King John's inconsistencies of leadership and vagaries of character. Changes in activity, matching those in mood, are core features of the condition. METHOD - A measure of King John's activity was derived from his travelling itinerary. Change Point Analysis (CPA) was used to detect significant changes in that travelling activity and from them, to identify clinically compliant, high and low, activity time periods. The results were tested against an alternative mathematical model (Bollinger Bands™), three alternative parameters and two comparator itineraries (familial & non-familial). Using primary historical sources and published analyses, bipolar symptoms were identified and their temporal relationship to the ICD-10 compliant CPA periods evaluated. The influence of circumstances was also evaluated using primary sources and a representative sequential sample (1200-1204). RESULTS - CPA identified 83 periods of changed travelling activity. These changes were mathematically independent of the availability of the historical sources that underpin the itinerary. From these, 37 high and 22 low periods complied with current diagnostic guidelines and demonstrated descriptive and statistical similarities to those found in the bipolar literature. Analyses using alternative mathematical modelling and different parameters showed similar changes; analyses of comparator itineraries showed a possible familial trait. Of the 17 bipolar symptoms identified, all were found in CPA periods of appropriate polarity. Of the 23 sequential periods, 10 showed evidence of behaviour that was difficult to attribute to circumstances. CONCLUSIONS & OUTCOMES - The pattern of changes in King John's activity are highly suggestive of bipolar disorder with primary historical sources describing synchronous bipolar behaviour. This may alter our understanding both of King John and of Magna Carta. Change Point Analysis merits greater consideration when analysing time based data, as does the use of activity as an objective marker of human behaviour.

The thesis aims at change-point estimation in gradual change models. Methods avail- able in literature are reviewed and modified for point-of-stabilisation (PoSt) context, present e.g. in drug continuous manufacturing. We describe in detail the estimation in the linear PoSt model and we extend the methods to quadratic and Emax model. We describe construction of confidence intervals for the change-point, discuss their interpre- tation and show how they can be used in practice. We also address the situation when the assumption of homoscedasticity is not fulfilled. Next, we run simulations to calculate the coverage of confidence intervals for the change-point in discussed models using asymp- totic results and bootstrap with different parameter combinations. We also inspect the simulated distribution of derived estimators with finite sample. In the last chapter, we discuss the situation when the model for the data is incorrectly specified and we calculate the coverage of confidence intervals using simulations. 1

No description available.

No description available.

No description available.

No description available.

Title: Detection of change in some special regression models Author: Bc. Petra Exnarová Department: Department of Probability and Mathematical Statistics Supervisor: Prof. RNDr. Marie Hušková, DrSc. Abstract: Presented thesis deals with testing of change in three special cases of change-point analysis. First of them is case of continuous change in linear regression (so-called broken-line model), the other two are related to change in parameters of discrete value distributions - simple case of Bernoulli distributed variables is studied first and then the approach is generalized for case of Multi- nomial distribution. Both situations of known and unknown change point are described for all three cases. Beside approximation by using limit theorems, the bootstrap method and permutation test are described for all studied cases as well. The comparison of critical values gained by different approaches for the particular tests and small power analysis is done using simulations. Keywords: change-point analysis, broken-line model, discrete distribution, boot- strap, permutation test 1

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.

The Objective of this thesis is to address some interesting problems in the Indian cellular services market. The first problem we address relates to identifying important change points that marked the evolution of the telecom market since Indian Independence. We use the data on per-capita availability of telephones in India to this effect. We identify important change points that mapped to the computerization move in 1989, the liberalization and globalization policies starting from 1991 and subsequently the introduction of NTP 1997 and NTP 1999. We also identify the important change points that mark the growth of cellular services subscriber base in India. We map change points detected to some of the important macro level policy initiatives that were taken by TRAI. The second problem we address is the assessment of policy interventions on the growth of cellular subscriber base in India. We model the impact of two important policy interventions namely, the NTP 1999 and its spill-over policy the entry of the fourth player into the market to offer services. We model the abrupt temporary, abrupt permanent and gradual permanent impacts of these interventions individually and in a coupled manner. We are arguably the first to use the intervention analysis and change point analysis to study the Indian telecom market. The third problem relates to the most challenging task of forecasting the growth of cellular services subscribers in India. We use novel machine learning techniques like ε-SVR and ν-SVR and compare its performance with ANN and ARIMA using standard performance metrics. Initially, we venture to predict the aggregate subscriber growth of cellular mobile subscribers in India using the SVR techniques. This would be of interest to the policy makers from a strategic standpoint. Subsequently, we predict the marginal(monthly) subscriber growth using SVR and tabulate the results for varying depths of forecasting which would be of interest to service providers form an operation standpoint. We find that the SVR techniques performed better than ANN and ARIMA particularly with respect to forward or out-sample forecasting when the time periods increase. The final problem involves a differential game model in an oligopoly set up for the telecom service providers who tried to optimize their advertisement innovation mix in order to maximize their discounted flow of profits. We consider the situation where the service providers make Cournot conjectures about the action of their rivals. The firms would not enter into agreements or form cartels. The firms choose the quantity they want to sell simultaneously. The essence of the Cournot conjecture was that though it was a quantity based competition, no single firm could unilaterally try to improve the total quantity sold in the market. Every firm made only one decision and did so when other firms were simultaneously making decisions. We have come across papers that considered either advertisement or product/process innovation separately but not together. We incorporate both these control variables with the inverse demand function as the state variable. We propose an open-loop solution that is dependent on time. We conduct experiments with various combinations of churn and spill-over rates of advertisement and innovation and thereby get some managerial insights.