Getting started -- PCA with more than two variables -- Scaling of data -- Inferential procedures -- Putting it all together -- hearing loss I -- Operations with group data -- Vector interpretation I: simplifications and inferential techniques -- Vector interpretation II: rotation -- A case history-hearing loss II -- Singular value decomposition: multidimensional scaling I -- Distance models: multidimensional scaling II -- Linear models I: regression; PCA of predictor Variables -- Linear models II: analysis of variance; PCA of response variables -- Other applications of PCA -- Flatland: special procedures for two dimensions -- Odds and ends -- What is factor analysis anyhow? -- Other competitors.
Applied Regression Including Computing and Graphics; Contents; Preface; PART I INTRODUCTION; 1 Looking Forward and Back; 2 Introduction to Regression; 3 Introduction to Smoothing; 4 Bivariate Distributions; 5 Two-Dimensional Plots; PART II. TOOLS; 6 Simple Linear Regression; 7 Introduction to Multiple Linear Regression; 8 Three-Dimensional Plots; 9 Weights and Lack-of-Fit; 10 Understanding Coefficients; 11 Relating Mean Functions; 12 Factors and Interactions; 13 Response Transformations; 14 Diagnostics I: Curvature and Nonconstant Variance; 15 Diagnostics II: Influence and Outliers.
This book contains 30 selected, refereed papers from an in- ternational conference on bootstrapping and related techni- ques held in Trier 1990. Thepurpose of the book is to in- form about recent research in the area of bootstrap, jack- knife and Monte Carlo Tests. Addressing the novice and the expert it covers as well theoretical as practical aspects of these statistical techniques. Potential users in different disciplines as biometry, epidemiology, computer science, economics and sociology but also theoretical researchers s- hould consult the book to be informed on the state of the art in this area
Dieses Lehrbuch gibt einen umfassenden Überblick über Methoden der deskriptiven Statistik, die durch einige Verfahren der explorativen Datenanalyse ergänzt wurden. Die zahlreichen statistischen Möglichkeiten zur Quantifizierung empirischer Phänomene werden problemorientiert dargestellt, wobei ihre Entwicklung schrittweise erfolgt, so daß Notwendigkeit und Nutzen der Vorgehensweise deutlich hervortreten. Dadurch soll ein fundiertes Verständnis für statistische Methoden geweckt werden. Dieses wird durch repräsentative Beispiele unterstützt. Übungsaufgaben mit Lösungen ergänzen den Text
Mit der Version 6.01 von SPSS für Windows steht das weltweit verbreitetste und mächtige Datenanalysesystem mit zahlreichen Erweiterungen und Verbesserungen nun auch unter einer deutschen Windows-Oberfläche zur Verfügung. Die Autoren, die in Lehre und Forschung langjährige Erfahrungen mit SPSS haben, bieten dem Anfänger eine Einführung und dem erfahrenen SPSS-Anwender eine umfassende Behandlung des Basissystems von SPSS für Windows 6.01. Alle Anwendungen werden ausführlich mit Beispielen aus der Praxis dargestellt. Dabei werden auch die statistischen Methoden und Verfahren mit ihren Anwendungsvoraussetzungen behandelt. Im Anhang aufgeführte Daten ermöglichen es, die meisten Anwendungen am PC nachzuvollziehen
Explains how Hilbert space techniques cross the boundaries into the foundations of probability and statistics. Focuses on the theory of martingales stochastic integration, interpolation and density estimation. Includes a copious amount of problems and examples.
This book describes highly applicable mathematics without using calculus or limits in general. The study agrees with the opinion that the traditional calculus/analysis is not necessarily the only proper grounding for academics who wish to apply mathematics. The choice of topics is based on a desire to present those facets of mathematics which will be useful to economists and social/behavioral scientists. The volume is divided into seven chapters. Chapter I presents a brief review of the solution of systems of linear equations by the use of matrices. Chapter III introduces the theory of probability. The rest of the book deals with new developments in mathematics such as linear and dynamic programming, the theory of networks and the theory of games. These developments are generally recognized as the most important field in the `new mathematics' and they also have specific applications in the management sciences
The subject of this book is the incorporation and integration of mathematical and statistical techniques and information science topics into the field of classification, data analysis, and knowledge organization. Readers will find survey papers as well as research papers and reports on newest results. The papers are a combination of theoretical issues and applications in special fields: Spatial Data Analysis, Economics, Medicine, Biology, and Linguistics
The article sketches the evolution of mathematical social sciences in Great Britain, focussing on Political Economy and Social Statistics. The formal methods which were later to become of greatest importance in these sciences (differential calculus and probability theory) were mainly imported from continental mathematics at the beginning of the 19th century. The emergence of Political Economy and the transformation of classical Political Arithmetic into Statistics roughly coincided with this "catching-up" process. Moreover, the "Cambridge Network of Scientists" (Cannon), with its protagonists Whewell, Herschel, Babbage and Peacock, played a central role in the adoption of French mathematics as well as in the early attempts to place the social sciences on a methodologically sound basis. Not surprisingly, the Cambridge Scientists (gathered mainly in the Cambridge Philosophical Society and the Cambridge Astronomical Society) were among the first to use mathematical methods in dealing with "the complicated conduct of our social and moral relations" (Herschel). However, the mathematicization of the social sciences cannot be seen as a smooth, continuous process of successively applying formal techniques to social phenomena. The application of the general equilibrium framework of analytical mechanics to the study of man's desires and actions, and the use of probability theory in explaining (not just describing) the synthesis and development of social aggregates, required an essential precondition: a new kind of analysis of "man", such as had emerged in geology and physiology since the late 1830s. Using the principles of natural selection and reflex action, it became possible to view human societies simultaneously as random samples and systems of forces, to which mathematical techniques now became reasonably applicable. The rise of Economics and Eugenics (founded by Jevons and Galton, respectively) towards the end of the 19th century can thus be perceived as a late consequence of this "anthropological turn". Therefore, the evolution of mathematical social sciences is not a symptom of a "mechanistic" view of man (usually associated with Cartesian epistomology), but simply another result of the very dissolving of classical "mathesis" (Foucault), which entailed the appearance of "man" as a privileged object of knowledge. ; The article sketches the evolution of mathematical social sciences in Great Britain, focussing on Political Economy and Social Statistics. The formal methods which were later to become of greatest importance in these sciences (differential calculus and probability theory) were mainly imported from continental mathematics at the beginning of the 19th century. The emergence of Political Economy and the transformation of classical Political Arithmetic into Statistics roughly coincided with this "catching-up" process. Moreover, the "Cambridge Network of Scientists" (Cannon), with its protagonists Whewell, Herschel, Babbage and Peacock, played a central role in the adoption of French mathematics as well as in the early attempts to place the social sciences on a methodologically sound basis. Not surprisingly, the Cambridge Scientists (gathered mainly in the Cambridge Philosophical Society and the Cambridge Astronomical Society) were among the first to use mathematical methods in dealing with "the complicated conduct of our social and moral relations" (Herschel). However, the mathematicization of the social sciences cannot be seen as a smooth, continuous process of successively applying formal techniques to social phenomena. The application of the general equilibrium framework of analytical mechanics to the study of man's desires and actions, and the use of probability theory in explaining (not just describing) the synthesis and development of social aggregates, required an essential precondition: a new kind of analysis of "man", such as had emerged in geology and physiology since the late 1830s. Using the principles of natural selection and reflex action, it became possible to view human societies simultaneously as random samples and systems of forces, to which mathematical techniques now became reasonably applicable. The rise of Economics and Eugenics (founded by Jevons and Galton, respectively) towards the end of the 19th century can thus be perceived as a late consequence of this "anthropological turn". Therefore, the evolution of mathematical social sciences is not a symptom of a "mechanistic" view of man (usually associated with Cartesian epistomology), but simply another result of the very dissolving of classical "mathesis" (Foucault), which entailed the appearance of "man" as a privileged object of knowledge.
Mendelssohn's Philosophical Writings, published in 1761, bring the metaphysical tradition to bear on the topic of 'sentiments' (defined as knowledge or awareness by way of the senses). Mendelssohn offers a nuanced defence of Leibniz's theodicy and conception of freedom, an examination of the ethics of suicide, an account of the 'mixed sentiments' so central to the tragic genre, a hypothesis about weakness of will, an elaboration of the main principles and types of art, a definition of sublimity and analysis of its basic forms, and, lastly, a brief tract on probability theory, aimed at rebutting Hume's scepticism. This volume also includes the essay 'On Evidence in Metaphysical Sciences', selected in 1763 by the Berlin Royal Academy of Sciences over all other submitted essays, including one by Kant, as the best answer to the question of whether metaphysical sciences are capable of the same sort and degree of evidence as mathematics
Explains that the focus of decision theory is on the mathematical models. These may be probability based; loss functions or other forms of statistical representations of judgements. Yet, much of decision theory does not lie entirely within any one discipline: it draws on psychology, economics, mathematics, statistics, social sciences and many other areas of study. Investigates investors' perceptions and attitudes towards real estate. Highlights the important difference between theoretical exposure levels and pragmatic business considerations. Suggests a prescriptive model to explore judgements, beliefs and preferences of decision makers and to inform decision making. Examines the concept of risk and its place in developing a prescriptive model. Maintains that a decision must be judged on factors other than the risk of a single outcome.
Sequential Stochastic Optimization provides mathematicians and applied researchers with a well-developed framework in which stochastic optimization problems can be formulated and solved. Offering much material that is either new or has never before appeared in book form, it lucidly presents a unified theory of optimal stopping and optimal sequential control of stochastic processes. This book has been carefully organized so that little prior knowledge of the subject is assumed; its only prerequisites are a standard graduate course in probability theory and some familiarity with discrete-paramet.