Probability and statistics Books

Book SynopsisThis book provides a concise introduction to the mathematical foundations of time series analysis, with an emphasis on mathematical clarity. The text is reduced to the essential logical core, mostly using the symbolic language of mathematics, thus enabling readers to very quickly grasp the essential reasoning behind time series analysis. It appeals to anybody wanting to understand time series in a precise, mathematical manner. It is suitable for graduate courses in time series analysis but is equally useful as a reference work for students and researchers alike.Trade Review“‘This book provides a concise introduction to the mathematical foundations of time series analysis, with an emphasis on mathematical clarity. … It appeals to anybody wanting to understand time series in a precise, mathematical manner. It is suitable for graduate courses in time series analysis but is equally useful as a reference work for students and researchers alike.’ … The book can be recommended to all readers, who are interested in this field.” (Ludwig Paditz, zbMath 1414.62001, 2019)“This book is a rigorous, mathematically clear and self-contained and quite complete text on time series analysis, suitable both for graduate courses and as a reference book for researchers and users of stochastic temporal models.” (Nazaré Mendes Lopes, Mathematical Reviews, December, 2018)“Beran (Univ. of Konstanz, Germany) presents the mathematical foundations of time series analysis at a level suitable for advanced graduate students and researchers in statistics. The presentation is extremely concise … . the book gives definitions, theorems, and proofs, along with a few exercises and solutions. … it may be useful to graduate students and researchers as a reference.” (B. Borchers, Choice, Vol. 56 (03), November, 2018)​Table of Contents1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 What is a time series? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Time series versus iid data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 Typical assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.1 Fundamental properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.1.1 Ergodic property with a constant limit . . . . . . . . . . . . . . . . . . . 52.1.2 Strict Stationarity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.1.3 Weak Stationarity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.1.4 Weak stationarity and Hilbert spaces . . . . . . . . . . . . . . . . . . . . 92.1.5 Ergodic processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252.1.6 Sufficient conditions for the a.s. ergodic property with a constant limit. . . . . . . . . . . 262.1.7 Sufficient conditions for the L2-ergodic property with a constant limit . .. . . . .. . . 272.2 Specific assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302.2.1 Gaussian processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302.2.2 Linear processes in L2(Ω) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312.2.3 Linear processes with E(X2t ) = ∞ . . . . . . . . . . . . . . . . . . . . . . 342.2.4 Multivariate linear processes . . . . . . . . . . . . . . . . . . . . . . . . . . . 372.2.5 Invertibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382.2.6 Restrictions on the dependence structure . . . . . . . . . . . . . . . . . 493 Defining probability measures for time series . . . . . . . . . . . . . . . . . . . . . . 553.1 Finite dimensional distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 553.2 Transformations and equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563.3 Conditions on the expected value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573.4 Conditions on the autocovariance function . . . . . . . . . . . . . . . . . . . . . . 583.4.1 Positive semidefinite functions . . . . . . . . . . . . . . . . . . . . . . . . . 593.4.2 Spectral distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 613.4.3 Calculation and properties of F and f . . . . . . . . . . . . . . . . .4 Spectral representation of univariate time series . . . . . . . . . . . . . . . . . . . 814.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 814.2 Harmonic processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 814.3 Extension to general processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 844.3.1 Stochastic integrals with respect to Z . . . . . . . . . . . . . . . . . . . . 844.3.2 Existence and definition of Z . . . . . . . . . . . . . . . . . . . . . . . . . . 894.3.3 Interpretation of the spectral representation . . . . . . . . . . . . . . 974.4 Further properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 984.4.1 Relationship between ReZ and ImZ . . . . . . . . . . . . . . . . . . . . 984.4.2 Frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 994.4.3 Overtones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 994.4.4 Why are frequencies restricted to the range [-π,π]? . . . . . . . 1004.5 Linear filters and the spectral representation . . . . . . . . . . . . . . . . . . . . 1034.5.1 Effect on the spectral representation . . . . . . . . . . . . . . . . . . . . . 1034.5.2 Elimination of Frequency Bands . . . . . . . . . . . . . . . . . . . . . . . 1075 Spectral representation of real valued vector time series . . . . . . . . . . . . 1095.1 Cross-spectrum and spectral representation . . . . . . . . . . . . . . . . . . . . . 1095.2 Coherence and phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1166 Univariate ARMA processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1276.1 Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1276.2 Stationary solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1276.3 Causal stationary solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1316.4 Causal invertible stationary solution . . . . . . . . . . . . . . . . . . . . . . . . . . . 1336.5 Autocovariances of ARMA processes . . . . . . . . . . . . . . . . . . . . . . . . . . 1346.5.1 Calculation by integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1346.5.2 Calculation using the autocovariance generating function . . . 1356.5.3 Calculation using the Wold representation . . . . . . . . . . . . . . . 1386.5.4 Recursive calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1396.5.5 Asymptotic decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1406.6 Integrated, seasonal and fractional ARMA and ARIMA processes . . 1476.6.1 Integrated processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1476.6.2 Seasonal ARMA processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1476.6.3 Fractional ARIMA processes . . . . . . . . . . . . . . . . . . . . . . . . . . 1486.7 Unit roots, spurious correlation, cointegration . . . . . . . . . . . . . . . . . . . 1597 Generalized autoregressive processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1637.1 Definition of generalized autoregressive processes . . . . . . . . . . . . . . . 1637.2 Stationary solution of generalized autoregressive equations . . . . . . . . 1647.3 Definition of VARMA processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1687.4 Stationary solution of VARMA equations . . . . . . . . . . . . . . . . . . . . . . 1697.5 Definition of GARCH processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1717.6 Stationary solution of GARCH equations . . . . . . . . . . . . . . . . . . . . . . . 1727.7 Definition of ARCH(∞) processes . . . . . . . . . . . . . . . . . . . . .7.8 Stationary solution of ARCH(∞) equations . . . . . . . . . . . . . . . . . . . . . 1778 Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1818.1 Best linear prediction given an infinite past . . . . . . . . . . . . . . . . . . . . . 1818.2 Predictability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1828.3 Construction of the Wold decomposition from f . . . . . . . . . . . . . . . . . 1878.4 Best linear prediction given a finite past . . . . . . . . . . . . . . . . . . . . . . . . 1909 Inference for µ, γ and F . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1959.1 Location estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1959.2 Linear regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1979.3 Nonparametric estimation of γ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2059.4 Nonparametric estimation of f . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21110 Parametric estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22710.1 Gaussian and quasi maximum likelihood estimation . . . . . . . . . . . . . . 22710.2 Whittle approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22910.3 Autoregressive approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23210.4 Model choice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 Subject Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245

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Book SynopsisFeedback control systems is an important course in aerospace engineering, chemical engineering, electrical engineering, mechanical engineering, and mechatronics engineering, to name just a few. Feedback control systems improve the system's behavior so the desired response can be acheived. The first course on control engineering deals with Continuous Time (CT) Linear Time Invariant (LTI) systems. Plenty of good textbooks on the subject are available on the market, so there is no need to add one more. This book does not focus on the control engineering theories as it is assumed that the reader is familiar with them, i.e., took/takes a course on control engineering, and now wants to learn the applications of MATLAB® in control engineering. The focus of this book is control engineering applications of MATLAB® for a first course on control engineering.Table of ContentsPreface.- Acknowledgments.- Introduction to MATLAB®.- Commonly Used Commands in Analysis of Control Systems.- Introduction to Simulink®.- Controller Design in MATLAB®.- Introduction to System Identification Toolbox™.- References.- Authors' Biographies.

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Book SynopsisA lot of digital ink has been spilled on "big data" over the past few years. Most of this surge owes its origin to the various types of unstructured data in the wild, among which the proliferation of text-heavy data is particularly overwhelming, attributed to the daily use of web documents, business reviews, news, social posts, etc., by so many people worldwide.A core challenge presents itself: How can one efficiently and effectively turn massive, unstructured text into structured representation so as to further lay the foundation for many other downstream text mining applications? In this book, we investigated one promising paradigm for representing unstructured text, that is, through automatically identifying high-quality phrases from innumerable documents. In contrast to a list of frequent n-grams without proper filtering, users are often more interested in results based on variable-length phrases with certain semantics such as scientific concepts, organizations, slogans, and so on. We propose new principles and powerful methodologies to achieve this goal, from the scenario where a user can provide meaningful guidance to a fully automated setting through distant learning. This book also introduces applications enabled by the mined phrases and points out some promising research directions.Table of ContentsAcknowledgments.- Introduction.- Quality Phrase Mining with User Guidance.- Automated Quality Phrase Mining.- Phrase Mining Applications.- Bibliography.- Authors' Biographies .

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Book Synopsis- Part I: Stochastics and Statistical Theory.- Strong Gaussian Approximations with Random Multipliers.- Selection of Parametric Copula Models in the Approximation of Copulas using Cramér-von Mises Divergence.- Multivariate Dependence Based on Diagonal Sections: Spearman’s Footrule and Related Measures.- Proportional Asymptotics of Piecewise Exponential Proportional Hazards Models.- On the Choice of the Two Tuning Parameters for Nonparametric Estimation of an Elliptical Distribution Generator.- Part II: Inference and Machine Learning.- Inference from Longitudinal Data by Clustering and Machine Learning.- The Use of Neural Networks and PCA Dimensionality Reduction in the Imputation of Missing Fragments in High-Dimensional Time Series.- Discrete-Valued Time Series and Recurrent Neural Network Response Functions.- Application of Model-Free Time-Series Segmentation to Study Sleep in Mice.- Part III: Detection of Patterns in Data.- Testing for Dependence by Using Ordinal Patterns: Survey and Perspectives.- On Some Properties and Testing of Benford’s Law.

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Book SynopsisThe monograph is devoted to one of the most important trends in contemporary mathematical physics, the investigation of evolution equations of many-particle systems of statistical mechanics. The book systematizes rigorous results obtained in this field in recent years, and it presents contemporary methods for the investigation of evolution equations of infinite-particle systems. The book is intended for experts in statistical physics, mathematical physics, and probability theory and for students of universities specialized in mathematics and physics.Trade Review"This book may be useful for advanced graduate students and for scientists who are interested in mathematical problems of the statistical mechanics and rare ed gasesow.?"Oleg A. Sinkevich in: Zentralblatt Math 1/2010<

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Book SynopsisThis textbook teaches crucial statistical methods to answer research questions using a unique range of statistical software programs, including MINITAB and R. This textbook is developed for undergraduate students in agriculture, nursing, biology and biomedical research. Graduate students will also find it to be a useful way to refresh their statistics skills and to reference software options. The unique combination of examples is approached using MINITAB and R for their individual strengths. Subjects covered include among others data description, probability distributions, experimental design, regression analysis, randomized design and biological assay. Unlike other biostatistics textbooks, this text also includes outliers, influential observations in regression and an introduction to survival analysis. Material is taken from the author's extensive teaching and research in Africa, USA and the UK. Sample problems, references and electronic supplementary material accompany each chapter.Table of Contents​Table of Contents attached as well. Introduction.- Frequency Distributions.- Numerical Description of Data.- Probability and Probability Distributions.- Estimation and Hypothesis Testing.- Regression Analysis.- Categorical Data Analysis.- Experimental Design.- The Completely Randomized Design.- The Randomized Complete Block Design.- Multiple Blocking Designs.- Analysis of Covariance.- Factorial Treatments Designs.- The Split-Plot Design.- Incomplete Block Design.- Quantal-Bioassay.- Repeated Measures Design.- Survival Analysis.

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Book SynopsisThis volume presents five different methods recently developed to tackle the large scale behavior of highly correlated random systems, such as spin glasses, random polymers, local times and loop soups and random matrices. These methods, presented in a series of lectures delivered within the Jean-Morlet initiative (Spring 2013), play a fundamental role in the current development of probability theory and statistical mechanics. The lectures were: Random Polymers by E. Bolthausen, Spontaneous Replica Symmetry Breaking and Interpolation Methods by F. Guerra, Derrida's Random Energy Models by N. Kistler, Isomorphism Theorems by J. Rosen and Spectral Properties of Wigner Matrices by B. Schlein.This book is the first in a co-edition between the Jean-Morlet Chair at CIRM and the Springer Lecture Notes in Mathematics which aims to collect together courses and lectures on cutting-edge subjects given during the term of the Jean-Morlet Chair, as well as new material produced in its wake. It is targeted at researchers, in particular PhD students and postdocs, working in probability theory and statistical physics.Table of Contents1 Random Polymers.- 2 Spontaneous replica symmetry breaking and interpolation methods for complex statistical mechanics systems.- 3 Derrida’s random energy models: from spin glasses to the extremes of correlated random fields.- 4 Isomorphism Theorems: Markov processes, Gaussian processes and beyond.- 5 Spectral properties of Wigner matrices.

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Book SynopsisEndlich verstehen Sie die ökonomischen Anwendungsmöglichkeiten und Funktionsweisen statistischer Wahrscheinlichkeiten im Betrieb! Dieses Buch vermittelt Ihnen die grundlegenden Verfahren der Wahrscheinlichkeitsrechnung als auch der Wahrscheinlichkeitsverteilungen und zeigt Ihnen deren praktische Anwendung in Betrieb und Ökonomie. Beispiele und Fragen mit Musterlösungen dienen dem weiteren Verständnis.Table of ContentsGrundlagen statistischer Wahrscheinlichkeiten in der Betriebswirtschaft: Grundbegriffe der Wahrscheinlichkeitsrechnung Diskrete Wahrscheinlichkeitsverteilungen - Binomial- und Hypergeometrische Verteilung Stetige Wahrscheinlichkeitsverteilung - Normalverteilung Intervallschätzung Notwendiger Stichprobenumfang Wahlforschung Hypothesentestverfahren Tabelle der Standardnormalverteilung Mathematische Grundlagen der induktiven Statistik Lösungen

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Book SynopsisIn den empirischen Sozialwissenschaften dienen die Methoden und Techniken der Statistik der Auswertung von Ergebnissen empirischer Untersuchungen und ermöglicht so die Beschreibung der quantitiativen Eigenschaften einer beobachteten und vollständig erfassten Gruppe. Das vorliegende Buch beschäftigt sich nahezu ausschließlich mit deskriptiver Statistik, welche sich mit der Aufbereitung und Beschreibung von Datenmengen und deren Verteilung befasst. Nach einer ausführlichen und grundlegenden Einführung in das Thema werden die wichtigsten Häufigkeitsverteilungen sowie die Maßzahlen zu deren Beschreibung dargestellt. Mit der linearen Einfachregression wird zuletzt der lineare funktionale Zusammenhang zweier Variabler erläutert. Zu jedem Kapitel gibt es Beispiele, Übungsaufgaben und eine Zusammenfassung. Im Anhang befinden sich mehrere Klausuren mit Lösungen, die in den letzten Jahren an der TU Dresden benutzt wurden.Table of Contents1 Grundlagen.- 1.1 Geisteswissenschaften und empirische Wissenschaften heute.- 1.2 Grundmethoden der empirischen Wissenschaften.- 1.2.1 Untersuchungsformen.- 1.2.2 Datenerhebungstechniken.- 1.2.3 Auswahlverfahren.- 1.3 Ablauf empirischer Sozialforschung: Der Forschungsprozess.- 1.3.1 Auswahl des Forschungsgegenstandes.- 1.3.2 Theoriebildung.- 1.3.3 Planung der Untersuchung.- 1.3.4 Durchführung der Untersuchung (Datenerhebung).- 1.3.5 Beschreibung und Zusammenfassung der Ergebnisse.- 1.3.6 Verallgemeinerung der Ergebnisse und Publikation.- 1.4 Einführung in die Forschungsstatistik.- 1.4.1 Statistische Gesetzmäßigkeiten.- 1.4.2 Grundlegende statistische Begriffe.- 1.4.3 Statistische Symbole.- 1.5 Begriff des Messens und der Messskalen.- 1.5.1 Der Begriff des Messens.- 1.5.2 Die Messniveaus.- 1.5.3 Die Bedeutung der Messniveaus für die Statistik.- 1.5.4 Gütekriterien der Messung.- Aufgaben.- 2 Empirische Häufigkeitsverteilungen.- 2.1 Häufigkeit und Verteilung.- 2.1.1 Das Aufstellen einer Häufigkeitstabelle.- 2.1.2 Absolute, relative und prozentuale Häufigkeiten.- 2.1.3 Die Häufigkeitsfunktion.- 2.1.4 Die Empirische Verteilungsfunktion.- 2.2 In Klassen eingeteilte Merkmale.- 2.2.1 Das Einteilen der Messwerte in Klassen.- 2.2.2 Aufstellen der Klassenhäufigkeiten.- 2.2.3 Offene Klassen.- 2.2.4 Exakte Klassengrenzen.- 2.2.5 Repräsentation einer Klasse durch die K1assenmitte.- 2.2.6 Informationsverlust durch Klasseneinteilung.- 2.3 Graphische Darstellungen von Häufigkeitsverteilungen.- 2.3.1 Das Stab-oder Balkendiagramm.- 2.3.2 Das Kreisdiagramm.- 2.3.3 Das Histogramm.- 2.3.4 Das Polygon.- 2.3.5 Typische Fonnen spezieller Verteilungen.- 2.4 Erkennen von Fehlinformation in statistischen Analysen.- 3 Maßzahlen eindimensionaler Verteilungen.- 3.1 Lageparameter.- 3.1.1 Das arithmetische Mittel.- 3.1.2 Der Median.- 3.1.3 Der Modus.- 3.1.4 Relative Positionen.- 3.1.5 Zulässige und optimale Lageparameter der einzelnen Messniveaus.- 3.2 Dispersionsparameter.- 3.2.1 Spannweite.- 3.2.2 Der (mittlere) Quartilabstand.- 3.2.3 Standardabweichung und Varianz.- 3.2.4 Der Variationskoeffizient zum Vergleich mehrerer Stichproben.- 3.2.5 Die Zusammenfassung von Varianzen.- 3.2.6 Gesamtvarianz, systematische Varianz und Fehlervarianz.- 3.2.7 Die Summe der quadratischen Abweichungen.- Aufgaben.- 4 Maßzahlen zweidimensionaler Verteilungen.- 4.1 Vorbemerkungen.- 4.1.1 Linearität.- 4.1.2 Die gemeinsame Verteilung.- 4.1.3 Ein einfaches Beispiel zur Darstellung bivariater Verteilungen.- 4.2 Korrelation.- 4.2.1 Intervallniveau.- 4.2.2 Ordinalniveau.- 4.3 Nomina1niveau.- 4.3.1 Tau (Goodman und Kruskal).- 4.3.2 Lambda.- 4.3.3 Kontingenzkoeffizient.- 4.3.4 Phi.- 4.3.5 Cramer’s V.- 4.4 Interpretation.- 5 Die lineare Einfachregression.- 5.1 Anpassen von Kurven.- 5.2 Vorhersage bei korrelierten Variablen.- 5.3 Methode der kleinsten Quadrate.- 5.3.1 Berechnung der Regressionsgeraden Gy/x.- 5.3.2 Berechnung der Regressionsgeraden Gx/y.- 5.4 Regressionskoeffizient, Korrelationskoeffizient und Varianz.- 5.5 Der Korrelationskoeffizient als Maß für die Güte der Regression.- 5.5.1 Die Varianz um die Regressionsgerade Sy/x2.- 5.5.2 Die Varianz auf der Regressionsgeraden $$ s_{\tilde y}^2 $$.- 5.6 Berechnung zweier Beispielaufgaben.- 5.6.1 Beispiel 1.- 5.6.2 Beispiel 2.- Weiterführende Literatur.- Anhang 1 Probeklausuren.- Anhang 2 Lösungen zu den Probeklausuren.

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Book SynopsisIsoperimetric, measure concentration and random process techniques appear at the basis of the modern understanding of Probability in Banach spaces. Based on these tools, the book presents a complete treatment of the main aspects of Probability in Banach spaces (integrability and limit theorems for vector valued random variables, boundedness and continuity of random processes) and of some of their links to Geometry of Banach spaces (via the type and cotype properties). Its purpose is to present some of the main aspects of this theory, from the foundations to the most important achievements. The main features of the investigation are the systematic use of isoperimetry and concentration of measure and abstract random process techniques (entropy and majorizing measures). Examples of these probabilistic tools and ideas to classical Banach space theory are further developed.Trade ReviewThis book gives an excellent, almost complete account of the whole subject of probability in Banach spaces, a branch of probability theory that has undergone vigorous development... There is no doubt in the reviewer's mind that this book [has] become a classic. MathSciNetAs the authors state, "this book tries to present some of the main aspects of the theory of probability in Banach spaces, from the foundation of the topic to the latest developments and current research questions''. The authors have succeeded admirably… This very comprehensive book develops a wide variety of the methods existing … in probability in Banach spaces. … It [has] become an event for mathematicians… Zentralblatt MATHTable of ContentsNotation.- 0. Isoperimetric Background and Generalities.- 1. Isoperimetric Inequalities and the Concentration of Measure Phenomenon.- 2. Generalities on Banach Space Valued Random Variables and Random Processes.- I. Banach Space Valued Random Variables and Their Strong Limiting Properties.- 3. Gaussian Random Variables.- 4. Rademacher Averages.- 5. Stable Random Variables.- 6 Sums of Independent Random Variables.- 7. The Strong Law of Large Numbers.- 8. The Law of the Iterated Logarithm.- II. Tightness of Vector Valued Random Variables and Regularity of Random Processes.- 9. Type and Cotype of Banach Spaces.- 10. The Central Limit Theorem.- 11. Regularity of Random Processes.- 12. Regularity of Gaussian and Stable Processes.- 13. Stationary Processes and Random Fourier Series.- 14. Empirical Process Methods in Probability in Banach Spaces.- 15. Applications to Banach Space Theory.- References.

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Book SynopsisThis monograph is the r st in Fuzzy Approximation Theory. It contains mostly the author s research work on fuzziness of the last ten years and relies a lot on [10]-[32] and it is a natural outgrowth of them. It belongs to the broader area of Fuzzy Mathematics. Chapters are self-contained and several advanced courses can be taught out of this book. We provide lots of applications but always within the framework of Fuzzy Mathematics. In each chapter is given background and motivations. A c- plete list of references is provided at the end. The topics covered are very diverse. In Chapter 1 we give an extensive basic background on Fuzziness and Fuzzy Real Analysis, as well a complete description of the book. In the following Chapters 2,3 we cover in deep Fuzzy Di?erentiation and Integ- tion Theory, e.g. we present Fuzzy Taylor Formulae. It follows Chapter 4 on Fuzzy Ostrowski Inequalities. Then in Chapters 5, 6 we present results on classical algebraic and trigonometric polynomial Fuzzy Approximation.Table of ContentsABOUT H-FUZZY DIFFERENTIATION.- ON FUZZY TAYLOR FORMULAE.- FUZZY OSTROWSKI INEQUALITIES.- A FUZZY TRIGONOMETRIC APPROXIMATION THEOREM OF WEIERSTRASS-TYPE.- ON BEST APPROXIMATION AND JACKSON-TYPE ESTIMATES BY GENERALIZED FUZZY POLYNOMIALS.- BASIC FUZZY KOROVKIN THEORY.- FUZZY TRIGONOMETRIC KOROVKIN THEORY.- FUZZY GLOBAL SMOOTHNESS PRESERVATION.- FUZZY KOROVKIN THEORY AND INEQUALITIES.- HIGHER ORDER FUZZY KOROVKIN THEORY USING INEQUALITIES.- FUZZY WAVELET LIKE OPERATORS.- ESTIMATES TO DISTANCES BETWEEN FUZZY WAVELET LIKE OPERATORS.- FUZZY APPROXIMATION BY FUZZY CONVOLUTION OPERATORS.- DEGREE OF APPROXIMATION OF FUZZY NEURAL NETWORK OPERATORS, UNIVARIATE CASE.- HIGHER DEGREE OF FUZZY APPROXIMATION BY FUZZY WAVELET TYPE AND NEURAL NETWORK OPERATORS.- FUZZY RANDOM KOROVKIN THEOREMS AND INEQUALITIES.- FUZZY-RANDOM NEURAL NETWORK APPROXIMATION OPERATORS, UNIVARIATE CASE.- -SUMMABILITY AND FUZZY KOROVKIN APPROXIMATION.- -SUMMABILITY AND FUZZY TRIGONOMETRIC KOROVKIN APPROXIMATION.- UNIFORM REAL AND FUZZY ESTIMATES FOR DISTANCES BETWEEN WAVELET TYPE OPERATORS AT REAL AND FUZZY ENVIRONMENT.

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Book SynopsisIn Part I of this report the pointwise derivation of scalar set functions is investigated, first along the lines of R. DE POSSEL (abstract derivation basis) and A. P. MORSE (blankets); later certain concrete situations (e. g. , the interval basis) are studied. The principal tool is a Vitali property, whose precise form depends on the derivation property studied. The "halo" (defined at the beginning of Part I, Ch. IV) properties can serve to establish a Vitali property, or sometimes produce directly a derivation property. The main results established are the theorem of JESSEN-MARCINKIEWICZ-ZYGMUND (Part I, Ch. V) and the theorem of A. P. MORSE on the universal derivability of star blankets (Ch. VI) . . In Part II, points are at first discarded; the setting is somatic. It opens by treating an increasing stochastic basis with directed index sets (Th. I. 3) on which premartingales, semimartingales and martingales are defined. Convergence theorems, due largely to K. KRICKEBERG, are obtained using various types of convergence: stochastic, in the mean, in Lp-spaces, in ORLICZ spaces, and according to the order relation. We may mention in particular Th. II. 4. 7 on the stochastic convergence of a submartingale of bounded variation. To each theorem for martingales and semi-martingales there corresponds a theorem in the atomic case in the theory of cell (abstract interval) functions. The derivates concerned are global. Finally, in Ch.Table of ContentsI Pointwise Derivation.- I: Derivation Bases.- 1. Setting and general notation.- 2. dePossel’s derivation basis.- 3. Examples of bases.- 4. Pretopological notions.- 5. Comparison lemmas.- II: Derivation Theorems for ?-additive Set Functions under Assumptions of the Vitali Type.- 1. The individual Vitali assumption.- 2. The individual full derivation theorem for Radon or ?-fmite ?-integrals.- 3. The individual full derivation theorem for Radon measures.- 4. Class derivation theorems.- 5. Relation to Younovitch’s derivation theorem.- 6. The strong Vitali property.- 7. Half-regular and regular branches of a derivation basis.- III: The Converse Problem I: Covering Properties Deduced from Derivation Properties of ?-additive Set Functions.- 1. dePossel’s equivalence theorem.- 2. A necessary and sufficient condition for a weak derivation basis to derive a ?-finite ?-measure (Radon measure) ?.- 3. Younovitch’s equivalence theorem.- 4. A converse theorem for bases deriving the ?(q)-functions, q ? 1.- IV: Halo Assumptions in Derivation Theory. Converse Problem II.- 1. A. P. Morse’s halo properties.- 2. Abstract version of the strong Vitali theorem modelled after Banach.- 3. Abstract version of the strong Vitali theorem modelled after Carathéodory.- 4. Weak halo evanescence condition.- 5. Further criteria for the validity of the Density Theorem involving the weak halo.- 6. An individual derivability condition of Busemann-Feller type.- 7. The weak halo property in general bases.- 8. Product invariance of a weak halo property.- V: The Interval Basis. The Theorem of Jessen-Marcin-Kiewicz-Zygmund.- 1. The interval basis as a weak derivation basis.- 2. Theorem of Jessen-Marcinkiewicz-Zygmund.- 3. Properties of the halo function as consequences of derivation properties.- 4. Saks’ counterexample.- 5. The parallelepipedon basis.- 6. Saks’ “rarity” theorem.- VI: A. P. Morse’s Blankets.- 1. Nets.- 2. Hives.- 3. Fundamental covering theorems.- 4. Star blankets.- II Martingales and Cell Functions.- I: Theory without an Intervening Measure.- 1. Additive functions.- 2. ?-additive functions.- 3. Premartingales, semi-martingales, and martingales.- 4. Ordered space of martingales of basis(??).- 5. Integrals of premartingales.- 6. Martingales and additive functions.- 7. ?-additive martingales.- 8. Induced martingales.- 9. Premartingales and cell functions.- 10. Integrals of cell functions.- 11. Convergence theorems for martingales of bounded variation when ? is a measure algebra.- II: Theory in a Measure Space without Vitali Conditions.- 1. Preliminaries.- 2. Absolutely continuous and singular premartingales.- 3. Stochastic processes.- 4. Stochastic convergence.- 5. Mean convergence of order 1.- 6. Convergence in Orlicz spaces.- 7. Cell functions.- III: Theory in a Measure Space with Vitali Conditions.- 1. Preliminaries and definitions.- 2. Vitali conditions.- 3. Order convergence of martingales.- 4. Necessity of the Vitali conditions.- 5. Order convergence of submartingales.- 6. Order convergence of cell functions.- IV: Applications.- 1. Pointwise setting.- 2. Specifically pointwise concepts and results. Convergence almost everywhere.- 3. Martingales in the classical sense.- 4. Product spaces.- 5. The Radon- Nikodym integrand defined as a derivate.- 6. Representation of the spaces Lx as spaces of cell functions.- 7. Pointwise derivation of cell functions.- 8. Examples of concrete cell bases.- 9. Stochastic bases on a group.- Complements.- 1°. Derivation of vector-valued integrals.- 2°. Functional derivatives.- 3°. Topologies generated by measures.- 4°. Vitali’s theorem for invariant measures.- 5°. Global derivatives in locally compact topological groups..- 6°. Submartingales with decreasing stochastic bases.- 7°. Vector-valued martingales and derivation.- 9°. Derivation of measures.

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Book SynopsisDie Statistik und ihre Anwendung in unserem Leben in 101 Stichwörtern kurz, prägnant und verständlich erklären kann nur Walter Krämer. Ob es um die Zusammensetzung der Arbeitslosenquote geht, Aktienkurse, Wahlprognosen, Intelligenzquotient, polizeiliche Kriminalstatistik oder um Klinische Studien und Big Data: Der Leser erhält genau die Informationen, die er benötigt, um im täglichen Leben mit Statistik sinnvoll umgehen zu können. Dazu muss man kein Rechen-As sein oder Mathematik studiert haben. Ein gesunder Menschenverstand und die Bereitschaft, den Tatsachen ohne Vorurteile ins Gesicht zu sehen reichen vollkommen aus, um die Kunst der Statistik schätzen zu lernen: den Schein vom Sein zu trennen und die Stecknadel im Heuhaufen zu finden. Dieses Buch ist ein gleichermaßen verständlicher, faszinierender, amüsanter wie auch und hilfreicher als Ratgeber für unseren täglichen Umgang mit Statistik: denn nur wer versteht kann mitreden und entlarven.Trade Review“... Das Lesen dieses statistischen Wörter- Büchleins wird jenen am meisten Freude bereiten und Nutzen bringen, die sich, selbst Nichtstatistiker, aus unterschiedlichen Gründen - sei es beruflich oder im Studium - mit dem Fach auseinandersetzen müssen. Für diese Leserschaft ist es absolut lesenswert, lehrreich und auch launig geschrieben - ein Krämer eben! ...” (Andreas Quatember, in: Austrian Journal of Statistics, Jg. 46, Heft 1, Februar 2017)“Praktisches alphabetisch sortiertes Nachschlagewerk ... Die Begriffe werden jeweils kurz, leicht verständlich und nachvollziehbar anhand kleiner Beispiele Erläutert …” (Sandra Fuchs, in: Psychologie FoxBlog, sanfuchs1979.wordpress.com, 25. Mai 2016)

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Book SynopsisVier von zehn oder jeder Vierte ...Ein Blick in eine beliebige Tageszeitung genügt: Statistiken sind ohne Zweifel ein wesentlicher Bestandteil unserer Informationsgesellschaft. Dennoch ist das Image des Faches Statistik denkbar schlecht. Die Diskrepanz zwischen offenkundiger Bedeutung und schlechtem Ruf beruht zum Teil auf dem fundamentalen Irrtum, die Qualität der statistischen Methoden mit der Qualität ihrer Anwendung zu verwechseln. Denn ob aus Unachtsamkeit, Unverständnis oder Unvermögen: In den Medien wird mit Statistiken allzu oft Des-Information statt Information betrieben. Dieses Buch lädt die Leser zu einer kritischen und amüsanten Irrfahrt durch falsche Schlagzeilen und unsinnige Interpretationen statistischer Ergebnisse in Tageszeitungen oder Zeitschriften ein. Staunen Sie darüber, dass ein Viertel aller Studierenden alkoholabhängig ist, dass Männer ihren Rasierern treuer sind als ihren Partnerinnen, dass höherer Schokoladenkonsum mehr Nobelpreisträger erzeugt – und warum das alles blanker Unsinn ist.Aber Achtung: Dieses Buch kann Sie zu einem mündigeren Zeitungsleser machen!Trade Review“... hochaktuell und vor allem sehr lesenswert. ... liefert Quatember mit seinem Buch das nötige Basiswissen ...” (Barbara Denscher, in: Flaneurin, flaneurin.at, Mai 2020)“… Ein amüsant zu lesendes Büchlein ... so facettenreich, dass es als Lehrbuch verbreiteter Fehler gelten kann.” (in: Wasser und Abfall, Jg. 17, Heft 12, Dezember 2015)“... Das Werk gibt einen systematischen Überblick über typische Fehler, bespricht sie ausführlich und erklärt die mathematischen Zusammenhänge dahinter ...” (Roland Pilous, in: Spektrum.de, 9. September 2015)Table of ContentsEs ist nicht alles Gold, was glänzt.- 101 % zufriedene Kunden.- Ein Bild sagt mehr als tausend Worte.- Unvergleichliche Mittelwerte.- Mit Statistik lässt sich alles beweisen!.- Die Repräsentativitätslüge.- Der PISA-Wahnsinn.- Tatort Lotto.- Einen hab ich noch!.

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Book SynopsisDieses Buch beschäftigt sich mit den praktischen Fragestellungen statistischer Erhebungen (= Surveys) wie sie sich etwa in der empirischen akademischen Forschung, der offiziellen Statistik oder der kommerziellen Markt- und Meinungsforschung stellen: Wodurch unterscheiden sich verschiedene Stichprobendesigns? Wie sind sie praktisch umzusetzen (z. B. mit der Statistik-Freeware R)? Wie lassen sich die Daten- und die Ergebnisqualität beeinflussen? Wie kompensiert man Nonresponse? Wie können nichtzufällige Stichprobenverfahren und Big Data-Analysen im Zusammenhang mit den Aufgaben der Survey-Statistik funktionieren? Die Vermittlung des Methodenverständnisses wird unterstützt durch die verständnisorientierte Veranschaulichung der Basisideen. Diese Anschaulichkeit wird durch einfache und daher gut nachvollziehbare Beispiele gestützt. Für die vorliegende 3. Auflage wurde das Buch vollständig überarbeitet und inhaltlich unter anderem um die Betrachtung des Spannungsfeldes zwischen Survey-Theorie und -Praxis, die Grundlagen des Simulationsansatzes der Survey-Statistik und eine Auseinandersetzung mit den sich zunehmender Beliebtheit erfreuenden nichtzufälligen Stichprobenverfahren (inklusive den damit verwandten Big Data-Generierungsprozessen) erweitert. Jedes Kapitel wird zudem durch Aufgabenstellungen ergänzt, deren Umsetzung mit der Software R angeleitet wird.Table of ContentsVom Teil aufs Ganze – Einführung in die Stichprobentheorie.- Die Mutter aller Zufallsstichprobenverfahren – Die uneingeschränkte Zufallsauswahl.- Es geht auch anders – Weitere Schätzmethoden.- Zerlegen macht’s genauer – Die geschichtete uneingeschränkte Zufallsauswahl.- Nahe Liegendes gemeinsam erheben spart Geld – Die uneingeschränkte Klumpenauswahl.- Nahe beisammen und doch auseinander – Die zweistufige uneingeschränkte Zufallsauswahl.- Grenzt an Zauberei – Die größenproportionale Zufallsauswahl.- Welcher Zweck heiligt solche Mittel? - Die nichtzufälligen Auswahlen.- Anhang.- Literatur.- Sachverzeichnis.

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Book SynopsisIn die 4. Auflage dieser Aufgabensammlung wurde eine in Aufgaben-Form gebrachte empirische Untersuchung über das Lotto 6 aus 49 aufgenommen, die auf der Auswertung von 1264 Lotto-Ausspielungen aus 25 Jahren beruht. Das Ergebnis lautet: Auch aus Sicht der Mathematischen Statistik gibt es rationale Tipp-Strategien. Sie lassen sich darauf gründen, daß die realen Lottospieler-Kollektive einem stark ausgeprägten Konsensverhalten folgen, das rationales individuelles Verhalten in der Form eines speziellen Gegen-den-Strom-Schwimmens ermöglicht. Allein die systematische Berücksichtigung einer einzigen kollektiv stark vernachlässigten Lottozahl - solche Zahlen werden als "Antikonsenszahlen" bezeichnet - hätte in den untersuchten Ausspielungen die mathematische Gewinn-Erwartung um ca. 30% erhöht gegenüber dem "Normal"-Wert von 50% des Einsatzes. Danach erscheint es hoch plausibel, daß Spieler, die ihre Tippreihen ausschließlich aus solchen "Antikonsenszahlen" bilden, sogar eine mathematische Gewinn-Erwartung erzielen können, die den Einsatz übersteigt. Ein Bereich solcher "Antikonsenszahlen" wird mit Hilfe eines statistischen Schätzverfahrens explizit bestimmt. Die praktische Nutzanwendung solcher Ergebnisse steht allerdings unter dem Vorbehalt, daß sich das kollektive Spielverhalten nicht signifikant ändert, z.B. weil es durch Informationen - wie die hier vorgelegten - gestört wird.Table of ContentsAufgabensammlung zur statistischen Methodenlehre und Wahrscheinlichkeitsrechnung.

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Book SynopsisTable of Contents1 Einleitung.- I Motivation, Asymptotik und Modifikationen von Kern- und Nearest-Neighbour-Schätzern.- 2 Von der nichtparametrischen Dichteschätzung zur nichtparametrischen Zeitreihenanalyse und Prognose.- 2.1 Nichtparametrische Dichteschätzung.- 2.2 Nichtparametrische Regression.- 2.3 Nichtparametrische Zeitreihenanalyse und Prognose.- 3 Asymptotische Eigenschaften von Kern- und Nearest-Neighbour-Schätzern.- 3.1 Modellannahmen zur Herleitung asymptotischer Eigenschaften.- 3.2 Asymptotische Eigenschaften bei unabhängigen Beobachtungen.- 3.3 Asymptotische Eigenschaften bei abhängigen Beobachtungen.- 4 Ein Lösungsansatz zum Problem der Dimensionalität.- 4.1 Prognose auf der Basis ähnlicher aber möglicherweise entfernter Verlaufsmuster.- 4.2 Verringerung des Einflusses allzu ferner Verlaufsmuster.- 5 Biasreduktion durch asymmetrische Kerne.- 5.1 Der Fall p=1.- 5.2 Übertragung auf höhere Dimensionen.- 6 Biasreduzierende und varianzreduzierende Mischungen von Kern- und NN-Schätzern.- 7 Robuste Kern- und NN-Schätzer.- 7.1 M-Schätzer.- 7.2 L-Schätzer.- 7.3 R-Schätzer.- 7.4 Weitere Verfahren der robusten Kern- und Nearest-Neighbour-Schätzung.- 8 Weitere Modifikationen und einige Bemerkungen zur Wahl der Glättungsparameter.- 8.1 Additive nichtparametrische Modelle.- 8.2 Twicing.- 8.3 Jackknifing von Kern- und Nearest- Neighbour-Schätzern.- 8.4 Polynomiale nichtparametrische Regression.- 8.5 Semiparametrische Zeitreihenmodelle.- 8.6 Einige Bemerkungen zur Wahl der Bandweite und der Anzahl der nächsten Nachbarn.- II Einige empirische Studien.- 9 Nichtparametrische Modellierung der Wasserführung der Ruhr.- 9.1 Die Daten.- 9.2 Prediktogramme.- 9.3 Kern- und NN-Schätzer.- 9.4 Modifizierte Kern- und NN-Schätzer.- 10 Nichtparametrische Modellierung der Leitfähigkeit eines niedersächsischen Flusses.- 10.1 Die Daten.- 10.2 Prognoseeigenschaften gewöhnlicher NN-Schätzer.- 10.3 Verwendung asymmetrischer Kernfunktionen.- 10.4 Einbeziehen ähnlicher aber möglicherweise entfernter Verläufe.- 11 Nichtparametrische Modellierung der Luftbelastung durch Schwefeldioxid und Stickstoffdioxid.- 11.1 Allgemeines.- 11.2 Die Daten.- 11.3 Prognosen.- 12 Abschließende Bemerkungen.- Abbildungsverzeichnis.- Tabellenverzeichnis.

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Book SynopsisOne SCI\'ice mathematics bas rendered the 'Et moi, ...si j'avait su comment en revcnir. je n'y serais point aile: human race. It bas put common sc:nsc back where it belongs, on the topmost shelf next Jules Verne to the dusty canister labelled 'discarded n- sense'. The series is divergent; therefore we may be able to do something with it. Eric T. Bell O. Hcavisidc Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non- linearities abound. Similarly. all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. :; 'One service logic has rendered com- puter science .. :; 'One service category theory has rendered mathematics .. :. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.Table of Contents0. Preliminary Informationh.- 0.1 Probability Space.- 0.2 Random Functions and Processes.- 0.3 Conditional Probabilities.- 0.4 Independence.- 1. Sums of Independent Random Variables.- 1.1 Main Inequalities.- 1.2 Renewal Scheme.- 1.3 Random Walks. Recurrence.- 1.4 Distribution of Ladder Functions.- 2. General Processes with Independent Increments (Random Measures).- 2.1 Nonnegative Random Measures with Independent Values (r.m.i.v.).- 2.2 Random Measures with Alternating Signs.- 2.3 Stochastic Integrals and Countably Additive r.m.i.v.- 2.4 Random Linear Functional and Generalized Functions.- 3. Processes with Independent Increments. General Properties.- 3.1 Decomposition of a Process. Properties of Sample Functions.- 3.2 Stochastically Continuous Processes.- 3.3 Properties of Sample Functions.- 3.4 Locally Homogeneous Processes with Independent Increments.- 4. Homogeneous Processes.- 4.1 General Properties.- 4.2 Additive Functionals.- 4.3 Composed Poisson Process.- 4.4 Homogeneous Processes in R.- 5. Multiplicative Processes.- 5.1 Definition and General Properties.- 5.2 Multiplicative Processes in Abelian Groups.- 5.3 Stochastic Semigroups of Linear Operators in Rd.- Notes.- References.

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Book SynopsisThis book provides a comprehensive introduction to methods and models for categorical data analysis and their applications in social science research. Companion website also available, at https://webspace.utexas.edu/dpowers/www/Trade Review.,." the first introductory text to cover, in a single volume, models and methods for discrete dependent variables, cross-classifications, and longitudinal data. A great strength of the text is the authors' informal yet sophisticated approach, which combines the discussion of general principles with illuminating and realistic empirical examples." -Roberto Mare, University of California, Los Angeles, USA "Teaching this book will be almost too easy. The prose is clear, the examples are well chosen, and the Web site provides practical details." -Michael Hout, University of California, Berkeley, USA An excellent job done by the authors. As with the first edition, Powers and Xie make the analysis of categorical data easy to understand. There are 7 chapters that are clearly written, begining with a review of simple linear regression, then going to loglinear models for contingency tables, models for ordinal and nominal dependent variables and models for event ocurrence (models for rates). The technical level is high enough to understand the theory behind the analysis and the interpretation of results. The inclusion of a new chapeter (ch.5) on multilevel models is very clearly written, and includes a short introduction to modern Bayesian modelling. Although there is not enough space for a complete introduction into this topic (which requires a high level of mathematical statistics) the authors refer to other books (like the one by Scott Lynch) for more detailed explanations (needed for a better understanding) of bayesian modelling in general. This book is a great addition to the library of students and scientists in areas like biology and sociology who want an explained compendium of (modern) techniques for analysing categorical data. Amazon review

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Book SynopsisBayes''s theorem is a tool for assessing how probable evidence makes some hypothesis. The papers in this volume consider the worth and applicability of the theorem. Richard Swinburne sets out the philosophical issues. Elliott Sober argues that there are other criteria for assessing hypotheses. Colin Howson, Philip Dawid and John Earman consider how the theorem can be used in statistical science, in weighing evidence in criminal trials, and in assessing evidence for the occurrence of miracles. David Miller argues for the worth of the probability calculus as a tool for measuring propensities in nature rather than the strength of evidence. The volume ends with the original paper containing the theorem, presented to the Royal Society in 1763.Trade ReviewReview from previous edition This is a high quality, concise collection of articles on the foundations of probability and statistics. ... The volume closes with an Appendix containing a very polished reproduction of Bayes's classic 'An Essay Towards the Solving a Problem in the Doctrine of Chances'. The Essay still reads very well, and it should be on every probabilist's 'must read' list. I feel quite comfortable saying something almost as glowing about this entire volume. I found this book very edifying and clear, and the debates and issues it encompasses are of great importance for contemporary philosophy of probability, statistics, and decision-making. I highly recommend this book to anyone with interests in these areas, and I commend Swinburne for putting together this neat little book. * Notre Dame Philosophical Review *Table of ContentsIntroduction ; Bayesianism - its scopes and limits ; Bayesianism in Statistics ; Bayes's Theorem and Weighing Evidence by Juries ; Bayes, Hume, Price, and Miracles ; Propensities May Satisfy Bayes's Theorem ; 'An Essay Towards Solving a Problem in the Doctrine of Chances' by Thomas Bayes, presented to the Royal Society by Richard Price. Preceded by a historical introduction by G A Barnard.

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Book SynopsisSuitable for those who needs to communicate complex research results, this title includes four new chapters that cover writing about interactions, writing about event history analysis, writing about multilevel models, and the Goldilocks principle for choosing the right size contrast for interpreting results for different variables.Trade Review"To assist readers in understanding the ideas, Jane E. Miller practices what she preaches, keeping text succinct, vocabulary accessible, and examples and analogies easy to relate to. The tome is chock full of 'Zen moments'." (Choice)"

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Book SynopsisHow Much Inequality Is Fair? synthesizes concepts from economics, political philosophy, game theory, information theory, statistical mechanics, and systems engineering into a mathematical framework for a fair free-market society. Venkat Venkatasubramanian compares his theory’s predictions to actual inequality data and discusses its implications.Trade ReviewVenkat Venkatasubramanian's unusual argument, which draws on both mathematical and philosophical principles to propose a model of a fair society, is itself worthy of remark. Whether or not you agree with it, it is clearly and fairly presented. It's one of the best books of its kind. -- Simon DeDeo, Carnegie Mellon University A thoughtful book, with unique philosophical insights, that is refreshing for the ways in which it is different from standard economic theory. It addresses one of the major questions of our day-indeed, of the past two hundred years-and does so in a readable, thought-provoking way. -- Robert Axtell, George Mason UniversityTable of ContentsList of TablesList of FiguresPreface1. Extreme Inequality in Income and Wealth2. Foundational Principles of a Fair Capitalist Society3. Distributive Justice in a Hybrid Utopia4. Statistical Thermodynamics and Equilibrium Distribution5. Fairness in Income Distribution6. Global Trends in Income Inequality: Theory Versus Reality7. What Is Fair Pay for Executives?8. Final Synthesis and Future DirectionsNotesBibliographyIndex

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Book SynopsisHow Much Inequality Is Fair? synthesizes concepts from economics, political philosophy, game theory, information theory, statistical mechanics, and systems engineering into a mathematical framework for a fair free-market society. Venkat Venkatasubramanian compares his theory’s predictions to actual inequality data and discusses its implications.Trade ReviewVenkat Venkatasubramanian’s unusual argument, which draws on both mathematical and philosophical principles to propose a model of a fair society, is itself worthy of remark. Whether or not you agree with it, it is clearly and fairly presented. It’s one of the best books of its kind. -- Simon DeDeo, Carnegie Mellon UniversityA thoughtful book, with unique philosophical insights, that is refreshing for the ways in which it is different from standard economic theory. It addresses one of the major questions of our day—indeed, of the past two hundred years—and does so in a readable, thought-provoking way. -- Robert Axtell, George Mason UniversityStands out in originality, interdisciplinary focus, and crisp phrasing. * Journal of Philosophical Economics *Table of ContentsList of TablesList of FiguresPreface1. Extreme Inequality in Income and Wealth2. Foundational Principles of a Fair Capitalist Society3. Distributive Justice in a Hybrid Utopia4. Statistical Thermodynamics and Equilibrium Distribution5. Fairness in Income Distribution6. Global Trends in Income Inequality: Theory Versus Reality7. What Is Fair Pay for Executives?8. Final Synthesis and Future DirectionsNotesBibliographyIndex

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Book SynopsisThis book describes how modern queuing theory can be applied to problems in telecommunication engineering. It starts with a survey of the essential theory behind Gaussian processes, large deviations, and queuing theory and then introduces the idea of a traffic processes in communication systems.Trade Review"The book maybe useful for specialists connected with queuing theory and working in applied probability." (Zentralblatt MATH, 2008)Table of ContentsPreface and acknowledgments. 1 Introduction. Part A: Gaussian traffic and large deviations. 2 The Gaussian source model. 2.1 Modeling network traffic. 2.2 Notation and preliminaries on Gaussian random variables. 2.3 Gaussian sources. 2.4 Generic examples-long-range dependence and smoothness. 2.5 Other useful Gaussian source models. 2.6 Applicability of Gaussian source models for network traffic. 3 Gaussian sources: validation, justification. 3.1 Validation. 3.2 Convergence of on-off traffic to a Gaussian process. 4 Large deviations for Gaussian processes. 4.1 Cram´er's theorem. 4.2 Schilder's theorem. Part B: Large deviations of Gaussian queues. 5 Gaussian queues: an introduction. 5.1 Lindley's recursion, the steady-state buffer content. 5.2 Gaussian queues. 5.3 Special cases: Brownian motion and Brownian bridge. 5.4 A powerful approximation. 5.5 Asymptotics. 5.6 Large-buffer asymptotics. 6 Logarithmic many-sources asymptotics. 6.1 Many-sources asymptotics: the loss curve. 6.2 Duality between loss curve and variance function. 6.3 The buffer-bandwidth curve is convex. 7 Exact many-sources asymptotics. 7.1 Slotted time: results. 7.2 Slotted time: proofs. 7.3 Continuous time: results. 7.4 Continuous time: proofs. 8 Simulation. 8.1 Determining the simulation horizon. 8.2 Importance sampling algorithms. 8.3 Asymptotic efficiency. 8.4 Efficient estimation of the overflow probability. 9 Tandem and priority queues. 9.1 Tandem: model and preliminaries. 9.2 Tandem: lower bound on the decay rate. 9.3 Tandem: tightness of the decay rate. 9.4 Tandem: properties of the input rate path. 9.5 Tandem: examples. 9.6 Priority queues. 10 Generalized processor sharing. 10.1 Preliminaries on GPS. 10.2 Generic upper and lower bound on the overflow probability. 10.3 Lower bound on the decay rate: class 2 in underload. 10.4 Upper bound on the decay rate: class 2 in underload. 10.5 Analysis of the decay rate: class 2 in overload. 10.6 Discussion of the results. 10.7 Delay asymptotics. 11 Explicit results for short-range dependent inputs. 11.1 Asymptotically linear variance; some preliminaries. 11.2 Tandem queue with srd input. 11.3 Priority queue with srd input. 11.4 GPS queue with srd input. 11.5 Concluding remarks. 12 Brownian queues. 12.1 Single queue: detailed results. 12.2 Tandem: distribution of the downstream queue. 12.3 Tandem: joint distribution. Part C: Applications. 13 Weight setting in GPS. 13.1 An optimal partitioning approach to weight setting. 13.2 Approximation of the overflow probabilities. 13.3 Fixed weights. 13.4 Realizable region. 14 A link dimensioning formula and empirical support. 14.1 Objectives, modeling, and analysis. 14.2 Numerical study. 14.3 Empirical study. 14.4 Implementation aspects. 15 Link dimensioning: indirect variance estimation. 15.1 Theoretical foundations. 15.2 Implementation issues. 15.3 Error analysis of the inversion procedure. 15.4 Validation. 16 A framework for bandwidth trading. 16.1 Bandwidth trading. 16.2 Model and preliminaries. 16.3 Single-link network. 16.4 Gaussian traffic; utility as a function of loss. 16.5 Sanov's theorem and its inverse. 16.6 Estimation of loss probabilities. 16.7 Numerical example. Bibliography. Index.

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Book SynopsisBayesian methods combine the evidence from the data at hand with previous quantitative knowledge to analyse practical problems in a wide range of areas. The calculations were previously complex, but it is now possible to routinely apply Bayesian methods due to advances in computing technology and the use of new sampling methods for estimating parameters. Such developments together with the availability of freeware such as WINBUGS and R have facilitated a rapid growth in the use of Bayesian methods, allowing their application in many scientific disciplines, including applied statistics, public health research, medical science, the social sciences and economics. Following the success of the first edition, this reworked and updated book provides an accessible approach to Bayesian computing and analysis, with an emphasis on the principles of prior selection, identification and the interpretation of real data sets. The second edition: Provides an Trade Review"This text is ideal for researchers in applied statistics, medical sciences, public health and the social sciences, who will benefit greatly from the examples and applications featured. The book will also appeal to graduate students of applied statistics, data analysis and Bayesian methods, and will provide a great source of reference for both researchers and students." (Zentralblatt MATH, 2010) Table of ContentsPreface. Chapter 1 Introduction: The Bayesian Method, its Benefits and Implementation. Chapter 2 Bayesian Model Choice, Comparison and Checking. Chapter 3 The Major Densities and their Application. Chapter 4 Normal Linear Regression, General Linear Models and Log-Linear Models. Chapter 5 Hierarchical Priors for Pooling Strength and Overdispersed Regression Modelling. Chapter 6 Discrete Mixture Priors. Chapter 7 Multinomial and Ordinal Regression Models. Chapter 8 Time Series Models. Chapter 9 Modelling Spatial Dependencies. Chapter 10 Nonlinear and Nonparametric Regression. Chapter 11 Multilevel and Panel Data Models. Chapter 12 Latent Variable and Structural Equation Models for Multivariate Data. Chapter 13 Survival and Event History Analysis. Chapter 14 Missing Data Models. Chapter 15 Measurement Error, Seemingly Unrelated Regressions, and Simultaneous Equations. Appendix 1 A Brief Guide to Using WINBUGS. Index.

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Book SynopsisThis guide offers an overview of the most common types of trial undertaken in early clinical development. The coverage discusses the different methodologies and the impact of new technologies, both clinical and statistical, on clinical development.Trade Review"An Introduction to Statistics in Early Phase Trials" is an admirably concise and practical guide to the pertinent context, principles and formulae for statisticians inexpert in the application of their discipline to Phase I and II clinical research". (Journal of Clinical Research Best Practices, 1 March 2011) “An Introduction to Statistics in Early Phase Trials provides concise descriptions of many early phase trial designs, along with the statistical equations necessary to gather and analyze the data” (Annals of Pharmacotherapy, 2010) "I enjoyed reading the work of Dr. Julious, Tan, and Machin,found it quite useful, and recommend it to others teaching about, working with, or considering work in the learning phase of drug development." (Journal of Biopharmaceutical Statistics, 2011) Table of ContentsChapter 1 Early phase trials 1 Chapter 2 Introduction to pharmacokinetics 13 Chapter 3 Sample size calculations for clinical trials 37 Chapter 4 Crossover trial basics 55 Chapter 5 Multi-period crossover trials 71 Chapter 6 First time into man 87 Chapter 7 Bayesian and frequentist methods 113 Chapter 8 First-time-into-new-population studies 125 Chapter 9 Bioequivalence studies 139 Chapter 10 Other Phase I trials 169 Chapter 11 Phase II trials: general issues 187 Chapter 12 Dose–response studies 197 Chapter 13 Phase II trials with toxic therapies 211 Chapter 14 Interpreting and applying early phase trial results 223 Chapter 15 Go/No-Go criteria 231 Appendix 245 References 251 Index 257

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Book SynopsisIn the evaluation of healthcare, rigorous methods of quantitative assessment are necessary to establish interventions that are beneficial, are superior to all alternatives and are cost-effective. Usually one study will not provide answers to these questions and it will be necessary to synthesize evidence from multiple sources.Table of ContentsPreface xi 1 Introduction 1 1.1 The rise of health economics 1 1.2 Decision making under uncertainty 4 1.2.1 Deterministic models 4 1.2.2 Probabilistic decision modelling 6 1.3 Evidence-based medicine 9 1.4 Bayesian statistics 10 1.5 NICE 11 1.6 Structure of the book 12 1.7 Summary key points 13 1.8 Further reading 13 References 14 2 Bayesian methods and WinBUGS 17 2.1 Introduction to Bayesian methods 17 2.1.1 What is a Bayesian approach? 17 2.1.2 Likelihood 18 2.1.3 Bayes’ theorem and Bayesian updating 19 2.1.4 Prior distributions 22 2.1.5 Summarising the posterior distribution 23 2.1.6 Prediction 24 2.1.7 More realistic and complex models 24 2.1.8 MCMC and Gibbs sampling 25 2.2 Introduction to WinBUGS 26 2.2.1 The BUGS language 26 2.2.2 Graphical representation 31 2.2.3 Running WinBUGS 32 2.2.4 Assessing convergence in WinBUGS 33 2.2.5 Statistical inference in WinBUGS 36 2.2.6 Practical aspects of using WinBUGS 39 2.3 Advantages and disadvantages of a Bayesian approach 39 2.4 Summary key points 40 2.5 Further reading 41 2.6 Exercises 41 References 42 3 Introduction to decision models 43 3.1 Introduction 43 3.2 Decision tree models 44 3.3 Model parameters 45 3.3.1 Effects of interventions 45 3.3.2 Quantities relating to the clinical epidemiology of the clinical condition being treated 50 3.3.3 Utilities 52 3.3.4 Resource use and costs 52 3.4 Deterministic decision tree 52 3.5 Stochastic decision tree 56 3.5.1 Presenting the results of stochastic economic decision models 60 3.6 Sources of evidence 66 3.7 Principles of synthesis for decision models (motivation for the rest of the book) 70 3.8 Summary key points 70 3.9 Further reading 71 3.10 Exercises 71 References 72 4 Meta-analysis using Bayesian methods 76 4.1 Introduction 76 4.2 Fixed Effect model 78 4.3 Random Effects model 81 4.3.1 The predictive distribution 83 4.3.2 Prior specification for τ 84 4.3.3 ‘Exact’ Random Effects model for Odds Ratios based on a Binomial likelihood 84 4.3.4 Shrunken study level estimates 86 4.4 Publication bias 87 4.5 Study validity 88 4.6 Summary key points 88 4.7 Further reading 88 4.8 Exercises 89 References 92 5 Exploring between study heterogeneity 94 5.1 Introduction 94 5.2 Random effects meta-regression models 95 5.2.1 Generic random effect meta-regression model 95 5.2.2 Random effects meta-regression model for Odds Ratio (OR) outcomes using a Binomial likelihood 98 5.2.3 Autocorrelation and centring covariates 100 5.3 Limitations of meta-regression 104 5.4 Baseline risk 105 5.4.1 Model for including baseline risk in a meta-regression on the (log) OR scale 107 5.4.2 Final comments on including baseline risk as a covariate 109 5.5 Summary key points 110 5.6 Further reading 110 5.7 Exercises 110 References 113 6 Model critique and evidence consistency in random effects meta-analysis 115 6.1 Introduction 115 6.2 The Random Effects model revisited 117 6.3 Assessing model fit 121 6.3.1 Deviance 121 6.3.2 Residual deviance 122 6.4 Model comparison 124 6.4.1 Effective number of parameters, pD 125 6.4.2 Deviance Information Criteria 126 6.5 Exploring inconsistency 127 6.5.1 Cross-validation 128 6.5.2 Mixed predictive checks 131 6.6 Summary key points 134 6.7 Further reading 134 6.8 Exercises 134 References 137 7 Evidence synthesis in a decision modelling framework 138 7.1 Introduction 138 7.2 Evaluation of decision models: One-stage vs two-stage approach 139 7.3 Sensitivity analyses (of model inputs and model specifications) 147 7.4 Summary key points 147 7.5 Further reading 147 7.6 Exercises 147 References 149 8 Multi-parameter evidence synthesis 151 8.1 Introduction 151 8.2 Prior and posterior simulation in a probabilistic model: Maple Syrup Urine Disease (MSUD) 152 8.3 A model for prenatal HIV testing 155 8.4 Model criticism in multi-parameter models 161 8.5 Evidence-based policy 163 8.6 Summary key points 164 8.7 Further reading 165 8.8 Exercises 166 References 167 9 Mixed and indirect treatment comparisons 169 9.1 Why go beyond ‘direct’ head-to-head trials? 169 9.2 A fixed treatment effects model for MTC 172 9.2.1 Absolute treatment effects 176 9.2.2 Relative treatment efficacy and ranking 176 9.3 Random Effects MTC models 178 9.4 Model choice and consistency of MTC evidence 179 9.4.1 Techniques for presenting and understanding the results of MTC 180 9.5 Multi-arm trials 181 9.6 Assumptions made in mixed treatment comparisons 182 9.7 Embedding an MTC within a cost-effectiveness analysis 183 9.8 Extension to continuous, rate and other outcomes 185 9.9 Summary key points 187 9.10 Further reading 187 9.11 Exercises 189 References 190 10 Markov models 193 10.1 Introduction 193 10.2 Continuous and discrete time Markov models 195 10.3 Decision analysis with Markov models 196 10.3.1 Evaluating Markov models 197 10.4 Estimating transition parameters from a single study 199 10.4.1 Likelihood 202 10.4.2 Priors and posteriors for multinomial probabilities 202 10.5 Propagating uncertainty in Markov parameters into a decision model 206 10.6 Estimating transition parameters from a synthesis of several studies 209 10.6.1 Challenges for meta-analysis of evidence on Markov transition parameters 209 10.6.2 The relationship between probabilities and rates 211 10.6.3 Modelling study effects 213 10.6.4 Synthesis of studies reporting aggregate data 215 10.6.5 Incorporating studies that provide event history data 217 10.6.6 Reporting results from a Random Effects model 219 10.6.7 Incorporating treatment effects 220 10.7 Summary key points 224 10.8 Further reading 224 10.9 Exercises 224 References 225 11 Generalised evidence synthesis 227 11.1 Introduction 227 11.2 Deriving a prior distribution from observational evidence 230 11.3 Bias allowance model for the observational data 233 11.4 Hierarchical models for evidence from different study designs 238 11.5 Discussion 244 11.6 Summary key points 244 11.7 Further reading 245 11.8 Exercises 246 References 248 12 Expected value of information for research prioritisation and study design 251 12.1 Introduction 251 12.2 Expected value of perfect information 256 12.3 Expected value of partial perfect information 259 12.3.1 Computation 261 12.3.2 Notes on EVPPI 264 12.4 Expected value of sample information 264 12.4.1 Computation 265 12.5 Expected net benefit of sampling 266 12.6 Summary key points 267 12.7 Further reading 268 12.8 Exercises 268 References 268 Appendix 1 Abbreviations 270 Appendix 2 Common distributions 272 A2.1 The Normal distribution 272 A2.2 The Binomial distribution 273 A2.3 The Multinomial distribution 273 A2.4 The Uniform distribution 274 A2.5 The Exponential distribution 274 A2.6 The Gamma distribution 275 A2.7 The Beta distribution 276 A2.8 The Dirichlet distribution 277 Index 278

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Book SynopsisAutoregressive Conditional Heteroskedastic (ARCH) processes are used in finance to model asset price volatility over time. This book introduces both the theory and applications of ARCH models and provides the basic theoretical and empirical background, before proceeding to more advanced issues and applications. The Authors provide coverage of the recent developments in ARCH modelling which can be implemented using econometric software, model construction, fitting and forecasting and model evaluation and selection. Key Features: Presents a comprehensive overview of both the theory and the practical applications of ARCH, an increasingly popular financial modelling technique. Assumes no prior knowledge of ARCH models; the basics such as model construction are introduced, before proceeding to more complex applications such as value-at-risk, option pricing and model evaluation. Uses empirical examples to demonstrate how the recent developments inTrade Review"Numerous articles on the Autoregressive Conditional Heteroskedastic (ARCH) process, an increasingly popular financial modeling technique, exist in various international journals. Now Xekalaki and Degiannakis (both statistics, Athens U. of Economics and Business, Greece) provide a thorough treatment of the ARCH theory and its practical applications, in a textbook for postgraduate and final-year undergraduate students which could serve as reference work for academics and financial market professionals." (Book News Inc, November 2010) Table of ContentsPrologue. Notation. 1 What is an ARCH process? 1.1 Introduction. 1.2 The Autoregressive Conditionally Heteroskedastic Process. 1.3 The Leverage Effect. 1.4 The Non-trading Period Effect. 1.5 Non-synchronous Trading Effect. 1.6 The Relationship between Conditional Variance and Conditional Mean. 2 ARCH Volatility Specifications. 2.1 Model Specifications. 2.2 Methods of Estimation. 2.3. Estimating the GARCH Model with EViews 6: An Empirical Example.. 2.4. Asymmetric Conditional Volatility Specifications. 2.5. Simulating ARCH Models Using EViews. 2.6. Estimating Asymmetric ARCH Models with G@RCH 4.2 OxMetrics – An Empirical Example.. 2.7. Misspecification Tests. 2.8 Other ARCH Volatility Specifications. 2.9 Other Methods of Volatility Modeling. 2.10 Interpretation of the ARCH Process. 3 Fractionally Integrated ARCH Models. 3.1 Fractionally Integrated ARCH Model Specifications. 3.2 Estimating Fractionally Integrated ARCH Models Using G@RCH 4.2 OxMetrics – An Empirical Example. 3.3 A More Detailed Investigation of the Normality of the Standardized Residuals – Goodness-of-fit Tests. 4 Volatility Forecasting: An Empirical Example Using EViews 6. 4.1 One-step-ahead Volatility Forecasting. 4.2 Ten-step-ahead Volatility Forecasting. 5 Other Distributional Assumptions. 5.1 Non-Normally Distributed Standardized Innovations. 5.2 Estimating ARCH Models with Non-Normally Distributed Standardized Innovations Using G@RCH 4.2 OxMetrics – An Empirical Example. 5.3 Estimating ARCH Models with Non-Normally Distributed Standardized Innovations Using EViews 6 – An Empirical Example. 5.4 Estimating ARCH Models with Non-Normally Distributed Standardized Innovations Using EViews 6 – The LogL Object. 6 Volatility Forecasting: An Empirical Example Using G@RCH Ox. 7 Intra-Day Realized Volatility Models. 7.1 Realized Volatility. 7.2 Intra-Day Volatility Models. 7.3 Intra-Day Realized Volatility & ARFIMAX Models in G@RCH 4.2 OxMetrics – An Empirical example. 8 Applications in Value-at-Risk, Expected Shortfalls, Options Pricing. 8.1 One-day-ahead Value-at-Risk Forecasting. 8.2 One-day-ahead Expected Shortfalls Forecasting. 8.3 FTSE100 Index: One-step-ahead Value-at-Risk and Expected Shortfall Forecasting. 8.4 Multi-period Value-at-Risk and Expected Shortfalls Forecasting. 8.5 ARCH Volatility Forecasts in Black and Scholes Option Pricing. 8.6 ARCH Option Pricing Formulas. 9 Implied Volatility Indices and ARCH Models. 9.1 Implied Volatility. 9.2 The VIX Index. 9.3 The Implied Volatility Index as an Explanatory Variable. 9.4 ARFIMAX Modeling for Implied Volatility Index. 10 ARCH Model Evaluation and Selection. 10.1 Evaluation of ARCH Models. 10.2 Selection of ARCH Models. 10.3 Application of Loss Functions as Methods of Model Selection.. 10.4 The SPA Test for VaR and Expected Shortfalls. 11 Multivariate ARCH Models. 11.1 Model Specifications. 11.2 Maximum Likelihood Estimation. 11.3 Estimating Multivariate ARCH Models Using EViews 6. 11.4 Estimating Multivariate ARCH Models Using G@RCH 5.0. 11.5 Evaluation of Multivariate ARCH Models. References. Author Index. Subject Index.

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Book SynopsisStatistical methodology plays a key role in ensuring that DNA evidence is collected, interpreted, analyzed and presented correctly. With the recent advances in computer technology, this methodology is more complex than ever before. There are a growing number of books in the area but none are devoted to the computational analysis of evidence. This book presents the methodology of statistical DNA forensics with an emphasis on the use of computational techniques to analyze and interpret forensic evidence.Table of ContentsPreface. List of figures. List of tables. 1. Introduction. 1.1 Statistics, forensic science and the law. 1.2 The use of statistics in forensic DNA. 1.3 Genetic basis of DNA profiling and typing technology. 1.3.1 Genetic basis. 1.3.2 Typing technology. 1.4 About the book. 2. Probability and statistics. 2.1 Probability. 2.2 Dependent events and conditional probability. 2.3 Law of total probability. 2.4 Bayes’ Theorem. 2.5 Binomial probability distribution. 2.6 Multinomial distribution. 2.7 Poisson distribution. 2.8 Normal distribution. 2.9 Likelihood ratio. 2.10 Statistical inference. 2.10.1 Test of hypothesis. 2.10.2 Estimation and testing. 2.11 Problems. 3. Population genetics. 3.1 Hardy-Weinberg equilibrium. 3.2 Test for Hardy-Weinberg equilibrium. 3.2.1 Observed and expected heterozygosities. 3.2.2 Chi-square test. 3.2.3 Fisher’s exact test. 3.2.4 Computer software. 3.3 Other statistics for analysis of a population database. 3.3.1 Linkage equilibrium. 3.3.2 Power of discrimination. 3.4 DNA profiling. 3.5 Subpopulation models. 3.6 Relatives. 3.7 Problems. 4. Parentage testing. 4.1 Standard trio. 4.1.1 Paternity index. 4.1.2 An example. 4.1.3 Posterior odds and probability of paternity. 4.2 Paternity computer software. 4.2.1 Steps in running the software. 4.2.2 The software to deal with an incest case. 4.3 A relative of the alleged father is the true father. 4.4 Alleged father unavailable but his relative is. 4.5 Motherless case. 4.5.1 Paternity index. 4.5.2 Computer software and example. 4.6 Motherless case: relatives involved. 4.6.1 A relative of the alleged father is the true father. 4.6.2 Alleged father unavailable but his relative is. 4.6.3 Computer software and example. 4.7 Determination of both parents. 4.8 Probability of excluding a random man from paternity. 4.9 Power of exclusion. 4.9.1 A random man case. 4.9.2 A relative case. 4.9.3 An elder brother case: mother available. 4.10 Other issues. 4.10.1 Reverse parentage. 4.10.2 Mutation. 4.11 Problems. 5. Testing for kinship. 5.1 Kinship testing of any two persons: HWE. 5.2 Computer software. 5.3 Kinship testing of two persons: subdivided populations. 5.3.1 Joint genotype probability. 5.3.2 Relatives involved. 5.4 Examples with software. 5.5 Three persons situation: HWE. 5.6 Computer software and example. 5.7 Three persons situation: subdivided populations. 5.7.1 Standard trio. 5.7.2 A relative of the alleged father is the true father. 5.7.3 Alleged father unavailable but his relative is. 5.7.4 Example. 5.7.5 General method and computer software. 5.8 Complex kinship determinations: method and software. 5.8.1 EasyPA_In_1_Minute software and the method. 5.8.2 EasyPAnt_In_1_Minute. 5.8.3 EasyIN_In_1_Minute. 5.8.4 EasyMISS_In_1_Minute. 5.8.5 Other considerations: probability of paternity and mutation. 5.9 Problems. 6. Interpreting mixtures. 6.1 An illustrative example. 6.2 Some common cases and a case example. 6.2.1 One victim, one suspect and one unknown. 6.2.2 One suspect and two unknowns. 6.2.3 Two suspects and two unknowns. 6.2.4 Case example. 6.2.5 Exclusion probability. 6.3 A general approach. 6.4 Population in Hardy-Weinberg equilibrium. 6.5 Population with multiple ethnic groups. 6.6 Subdivided population. 6.6.1 Single ethnic group: simple cases. 6.6.2 Single ethnic group: general situations. 6.6.3 Multiple ethnic groups. 6.7 Computer software and example. 6.8 NRC II Recommendation 4.1. 6.8.1 Single ethnic group. 6.8.2 Multiple ethnic groups. 6.9 Proofs. 6.9.1 The proof of Equation (6.6). 6.9.2 The proof of Equation (6.8). 6.9.3 The proof of Equation (6.9). 6.9.4 The proofs of Equations (6.11) and (6.12). 6.9.5 The proofs of Equations (6.14) and (6.15). 6.10 Problems. 7. Interpreting mixtures in the presence of relatives. 7.1 One pair of relatives: HWE. 7.1.1 Motivating example. 7.1.2 A probability formula. 7.1.3 Tested suspect with an unknown relative. 7.1.4 Unknown suspect with a tested relative. 7.1.5 Two related persons were unknown contributors. 7.1.6 An application. 7.2 Two pairs of relatives: HWE. 7.2.1 Two unknowns related respectively to two typed persons. 7.2.2 One unknown is related to a typed person and two other. unknowns are related. 7.2.3 Two pairs of related unknowns. 7.2.4 Examples. 7.2.5 Extension. 7.3 Related people from the same subdivided population. 7.3.1 Introductory example. 7.3.2 A simple case with one victim, one suspect and one relative. 7.3.3 General formulas. 7.3.4 An example analyzed by the software. 7.4 Proofs. 7.4.1 Preliminary. 7.4.2 The proof of Equation (7.5). 7.4.3 The proof of Equation (7.7). 7.4.4 The proof of Equation (7.9). 7.4.5 The proof of Equation (7.11). 7.4.6 The proof of Equation (7.13). 7.4.7 The proofs of Equations (7.18) and (7.20). 7.5 Problems. 8. Other issues. 8.1 Lineage markers. 8.2 Haplotypic genetic markers for mixture. 8.3 Bayesian network. 8.4 Peak information. 8.5 Mass disaster. 8.6 Database search. Solutions to Problems. Appendix A: The standard normal distribution. Appendix B: Upper 1% and 5% points of w2 distributions. Bibliography. Index.

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Book SynopsisAn up-to-date and comprehensive treatment of biosurveillance techniques With the worldwide awareness of bioterrorism and drug-resistant infectious diseases, the need for surveillance systems to accurately detect emerging epidemicsis essential for maintaining global safety.Trade Review“The book is especially valuable for anyone interested in automated disease surveillance because of its broad scope addressing all issues related to developing and operating automated disease surveillance systems.” (Biometrics, June 2009 ) "This book is essential reading for those learning about public health disease surveillance and for statisticians working with public health professional to improve the sensitivity, specificity, timeliness and cost-effectiveness of current surveillance systems." (Journal of the American Statistical Association, June 2008) "…creates a roadmap for scientists to follow…" (Electric Review, June/July 2007)Table of Contents1. Disease Surveillance (J. Lombardo & D. Ross). 2. Understanding the Data (S. Babin, et al.). 3. Obtaining the Data (R. Wojcik, et al.). 4. Alerting Algorithms for Biosurveillance (H. Burkom). 5. Putting It Together (L. Hauenstein, et al.). 6. Modern Disease Surveillance (S. Lewis, et al.). 7. Canadian Applications (J. Aramini & S. Mukhi). 8. Telehealth in England and Wales (D. Cooper). 9. EWORS amd Alerta DISAMAR (J. Chretien, et al.). 10. Evaulating Automated Surveillance Systems (D. Buckeridge, et al.). 11. Educating the Workforce (H. Lehmann). 12. The Road Ahead (J. Lombardo). Index.

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Book SynopsisThis book provides an overview of available methods for bioequivalence studies, adopting a practical approach via numerous examples using real data. All medical/pharmacokinetic background is provided, so that the book is suitable for both medical practitioners/pharmaceutical scientists, and biometricians.Trade Review"The book provides an excellent introduction for researchers approaching the concept of bioequivalence and is a complete and useful compendium for experienced statisticians." (Biometrical Journal, April 2009) "The book provides an important reference providing many worked examples with real data from drug development. Professionals from the harmaceutical industry and regulatory bodies will particularly appreciate the emphasis made on regulatory guidelines." (Statistical Methods in Medical Research, February 2009) "Bioequivalence Studies in Drug Development: Methods and Applications is an informative, timely, and easy-to-read contribution to bioequivalence and drug-drug/food-drug interaction literature." (Journal of the American Statistical Association, September 2008) "…those statisticians working in this area of research will find that this book will serve as an excellent reference for their work..." (Journal of Biopharmaceutical Statistics, January 2008) "This book would be beneficial to both pharmaceutical scientists/researchers and biostatisticians…" (Biometrics, September 2007) "For anyone interested in any aspect of bioequivalence, the book is a very valuable reference." (International Statistical Review, 2007) "…my pleasure to review…I would like to add this book to my book collection of pharmaceutical research and development." (Biometrics, September 2007)Table of ContentsPreface. 1 Introduction. 1.1 Definitions. 1.2 When are bioequivalence studies performed. 1.3 Design and conduct of bioequivalence studies. 1.4 Aims and structure of the book. References. 2 Metrics to characterize concentration-time profiles in single- and multiple-dose bioequivalence studies. 2.1 Introduction. 2.2 Pharmacokinetic characteristics (metrics) for single-dose studies. 2.3 Pharmacokinetic rate and extent characteristics (metrics) for multiple-dose studies. 2.4 Conclusions. References. 3 Basic statistical considerations. 3.1 Introduction. 3.2 Additive and multiplicative model. 3.3 Hypotheses testing. 3.4 The RT/TR crossover design assuming an additive model. References. 4 Assessment of average bioequivalence in the RT/TR design. 4.1 Introduction. 4.2 The RT/TR crossover design assuming a multiplicative model. 4.3 Test procedures for bioequivalence assessment. 4.4 Conclusions. References. 5 Power and sample size determination for testing average bioequivalence in the RT/TR design. 5.1 Introduction. 5.2 Challenging the classical approach. 5.3 Exact power and sample size calculation. 5.4 Modified acceptance ranges. 5.5 Approximate formulas for sample size calculation. 5.6 Exact power and sample size calculation by nQuery®. References. Appendix. 6 Presentation of bioequivalence studies. 6.1 Introduction. 6.2 Results from a single-dose study. 6.3 Results from a multiple-dose study. 6.4 Conclusions. References. 7 Designs with more than two formulations. 7.1 Introduction. 7.2 Williams designs. 7.3 Example: Dose linearity study. 7.4 Multiplicity. 7.5 Conclusions. References. 8 Analysis of pharmacokinetic interactions. 8.1 Introduction. 8.2 Pharmacokinetic drug-drug interaction studies. 8.3 Pharmacokinetic food-drug interactions. 8.4 Goal posts for drug interaction studies including no effect boundaries. 8.5 Labeling. 8.6 Conclusions. References. 9 Population and individual bioequivalence. 9.1 Introduction. 9.2 Brief history. 9.3 Study designs and statistical models. 9.4 Population bioequivalence. 9.5 Individual bioequivalence. 9.6 Disaggregate criteria. 9.7 Other approaches. 9.8 Average bioequivalence in replicate designs. 9.9 Example: The anti-hypertensive patch dataset. 9.10 Conclusions. References. 10 Equivalence assessment in case of clinical endpoints. 10.1 Introduction. 10.2 Design and testing procedure. 10.3 Power and sample size calculation. 10.4 Conclusions. Apendix. References. Index.

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Book SynopsisThis groundbreaking book introduces the application of statistical methodologies to e-Commerce data With the expanding presence of technology in today''s economic market, the use of the Internet for buying, selling, and investing is growing more popular and public in nature. Statistical Methods in e-Commerce Research is the first book of its kind to focus on the statistical models and methods that are essential in order to analyze information from electronic-commerce (e-Commerce) transactions, identify the challenges that arise with new e-Commerce data structures, and discover new knowledge about consumer activity. This collection gathers over thirty researchers and practitioners from the fields of statistics, computer science, information systems, and marketing to discuss the growing use of statistical methods in e-Commerce research. From privacy protection to economic impact, the book first identifies the many obstacles that are encountered while collecting,Table of ContentsPreface. Acknowledgements. Contributor List. Section I: Overview of E-Commerce Research Challenges. 1. Statistical Challenges in Internet Advertising (Deepak Agarwal). 2. How Has E-Commerce Research Advanced Understanding of the Offline World (Chris Forman and Avi Goldfarb)? 3. The Economic Impact of User-Generated and Firm-Generated Online Content: Directions for Advancing the Frontiers in Electronic Commerce Research (Anindya Ghose). 4. Is Privacy Protection for Data in an E-Commerce World an Oxymoron (Stephen E. Fienberg)? 5. Network Analysis of Wikipedia (Robert H. Warren, Edoardo M. Airoldi, and David L. Banks). Section II: E-Commerce Applications. 6. An Analysis of Price Dynamics, Bidder Networks, and Market Structure in Online Art Auctions (Mayukh Dass and Srinivas K. Reddy). 7. Modeling Web Usability Diagnostics on the Basis of Usage Statistics (Avi Harel, Ron S. Kenett, and Fabrizio Ruggeri). 8. Developing Rich Insights on Public Internet Firm Entry and Exit Based on Survival Analysis and Data Visualization (Robert J. Kauffman and Bin Wang). 9. Modeling Time-Varying Coefficients in Pooled Cross-Sectional E-Commerce Data: An Introduction (Eric Overby and Benn Konsynski). 10. Optimization of Search Engine Marketing Bidding Strategies Using Statistical Techniques (Alon Matas and Yoni Schamroth). Section III: New Methods For E-Commerce Data. 11. Clustering Data with Measurement Errors (Mahesh Kumar and Nitin R. Patel). 12. Functional Data Analysis for Sparse Auction Data (Bitao Liu and Hans-Georg Müller). 13. A Family of Growth Models for Representing the Price Process in Online Auctions (Valerie Hyde, Galit Shmueli, and Wolfgang Jank). 14. Models of Bidder Activity Consistent with Self-Similar Bid Arrivals (Ralph P. Russo, Galit Shmueli, and Nariankadu D. Shyamalkumar). 15. Dynamic Spatial Models for Online Markets (Wolfgang Jank and P.K. Kannan). 16. Differential Equation Trees to Model Price Dynamics in Online Auctions (Wolfgang Jank, Galit Shmueli, and Shanshan Wang). 17. Quantile Modeling for Wallet Estimation (Claudia Perlich and Saharon Rosset). 18. Applications of Randomized Response Methodology in E-Commerce (Peter G.M. van der Heijden and Ulf Böckenholt). Index.

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Book SynopsisPraise for the First Edition: For a beginner [this book] is a treasure trove; for an experienced person it can provide new ideas on how better to pursue the subject of applied statistics. Journal of Quality Technology Sensibly organized for quick reference, Statistical Rules of Thumb, Second Edition compiles simple rules that are widely applicable, robust, and elegant, and each captures key statistical concepts. This unique guide to the use of statistics for designing, conducting, and analyzing research studies illustrates real-world statistical applications through examples from fields such as public health and environmental studies. Along with an insightful discussion of the reasoning behind every technique, this easy-to-use handbook also conveys the various possibilities statisticians must think of when designing and conducting a study or analyzing its data. Each chapter presents clearly defined rules related to inference, covariatTrade Review?This is a unique and effective contribution. Unlike some statistical books, this is a truly enjoyable read.? (Doody?s Reviews) "For the applied researcher who does much of her or his own data analysis, this book is a must-have. Even the applied statistician would benefit from owning a copy of this collection. It is certain that some 'rules' will be new, and the descriptions in the text can come in quite handy when one i trying to explain a concept to a non-statistician. In short, this collection of 'rules' is highly recommended." (MAA Reviews, December 10, 2008) "For the applied researcher who does much of her or his own data analysis, this book is a must-have. Even the applied statistician would benefit from owning a copy of this collection. It is certain that some 'rules' will be new, and the descriptions in the text can come in quite handy when one is trying to explain a concept to a non-statistician. In short, this collection of 'rules' is highly recommended." (MAA Reviews, Dec 2008)Table of ContentsPreface to the Second Edition. Preface to the First Edition. Acronyms. 1. The Basics. 1.1 Four Basic Questions. 1.2 Observation is Selection. 1.3 Replicate to Characterize Variability. 1.4 Variability Occurs at Multiple Levels. 1.5 Invalid Selection is the Primary Threat to Valid Inference. 1.6 There is Variation in Strength of Inference. 1.7 Distinguish Randomized and Observational Studies. 1.8 Beware of Linear Models. 1.9 Keep Models As Simple As Possible, But Not More Simple. 1.10 Understand Omnibus Quantities. 1.11 Do Not Multiply Probabilities More Than Necessary. 1.12 Use Two-sided p-Values. 1.13 p-Values for Sample Size, Confidence Intervals for Results. 1.14 At Least Twelve Observations for a Confidence Interval. 1.15 Estimate ± Two Standard Errors is Remarkably Robust. 1.16 Know the Unit of the Variable. 1.17 Be Flexible About Scale of Measurement Determining Analysis. 1.18 Be Eclectic and Ecumenical in Influence. 2. Sample Size. 2.1 Begin with a Basic Formula for Sample Size-Lehr’s Equation. 2.2 Calculating Sample Size Using the Coefficient of Variation. 2.3 No Finite Population Correction for Survey Sample Size. 2.4 Standard Deviation and Sample Range. 2.5 Do Not Formulate a Study Solely in Terms of Effect Size. 2.6 Overlapping Confidence Intervals Do Not Imply Nonsignificance. 2.7 Sample Size Calculation for the Poisson Distribution. 2.8 Sample Size for Poisson with Background Rate. 2.9 Sample Size Calculation for the Binomial Distribution. 2.10 When Unequal Sample Sizes Matters; When They Don’t. 2.11 Sample Size With Different Costs for the Two Samples. 2.12 The Rule of Threes for 95% Upper Bounds When There Are No Events. 2.13 Sample Size Calculations Are Determined by the Analysis. 3. Observational Studies. 3.1 The Model for an Observational Study is the Sample Survey. 3.2 Large Sample Size Does Not Guarantee Validity. 3.3 Good Observational Studies Are Designed. 3.4 To Establish Cause Effect Requires Longitudinal Data. 3.5 Make Theories Elaborate to Establish Cause and Effect. 3.6 The Hill Guidelines Are a Useful Guide to Show Cause Effect. 3.7 Sensitivity Analyses Assess Models Uncertainty and Missing Data. 4. Covariation. 4.1 Assessing and Describing Covariation. 4.2 Don’t Summarize Regression Sampling Schemes. 4.3 Do Not Correlate Rates or Ratios Indiscriminately. 4.4 Determining Sample Size to Estimate a Correlation. 4.5 Pairing Data is not Always Good. 4.6 Go Beyond Correlation in Drawing Conclusions. 4.7 Agreement As Accuracy, Scale Differential, and Precision. 4.8 Assess Test Reliability by Means of Agreement. 4.9 Range of the Predictor Variable and Regression. 4.10 Measuring Change: Width More Important than Numbers. 5. Environmental Studies. 5.1 Begin with the Lognormal Distributions in Environmental Studies. 5.2 Differences Are More Symmetrical. 5.3 Know the Sample Space for Statements of Risk. 5.4 Beware of Pseudoreplication. 5.5 Think Beyond Simple Random Sampling. 5.6 The Size of the Population and Small Effects. 5.7 Models of Small Effects Are Sensitive to Assumptions. 5.8 Distinguish Between Variability and Uncertainty. 5.9 Description of the Database is As Important as Its Data. 5.10 Always Assess the Statistical Basis for an Environmental Standard. 5.11 Measurement of a Standard and Policy. 5.12 Parametric Analyses Make Maximum Use of the Data. 5.13 Confidence, Prediction, and Tolerance Intervals. 5.14 Statistics and Risk Assessment. 5.15 Exposure Assessment is the Weak Link in Assessing Health Effects of Pollutants. 5.16 Assess the Errors in Calibration Due to Inverse Regression. 6. Epidemiology. 6.1 Start with the Poisson to Model Incidence or Prevalence. 6.2 The Odds Ratio Approximates the Relative Risk Assuming the Disease is Rare. 6.3 The Number of Events is Crucial in Estimating Sample Size. 6.4 Use a Logarithmic Formulation to Calculate Sample Size. 6.5 Take No More than Four or Five Controls per Case. 6.6 Obtain at Least Ten Subjects for Every Variable Investigated. 6.7 Begin with Two Exponential Distribution to Model Time to Event. 6.8 Begin with Two Exponentials for Comparing Survival Times. 6.9 Be Wary of Surrogates. 6.10 Prevalence Dominates in Screening Rare Diseases. 6.11 Do Not Dichotomize Unless Absolutely Necessary. 6.12 Additive and Multiplicative Models. 7. Evidence-Based Medicine. 7.1 Strength of Evidence. 7.2 Relevance of Information: POEM vs. DOE. 7.3 Begin with Absolute Risk Reduction, then follow with Relative Risk. 7.4 The Number Needed to Treat (NNT) is Clinically Useful. 7.5 Variability in Response to Treatment Needs to be Considered. 7.6 Safety is the Weak Component of EBM. 7.7 Intent to Treat is the Default Analysis. 7.8 Use Prior Information but not Priors. 7.9 The Four Key Questions for Meta-analysis. 8. Design, Conduct, and Analysis. 8.1 Randomization Puts Systematic Effects into the Error Term. 8.2 Blocking is the Key to Reducing Variability. 8.3 Factorial Designs and Joint Effects. 8.4 High-Order Interactions Occur Rarely. 8.5 Balanced Designs Allow Easy Assessment of Joint Effects. 8.6 Analysis Follows Designs. 8.7 Independence, Equal Variance, and Normality. 8.8 Plan to Graph the Results of an Analysis. 8.9 Distinguish Between Design Structure and Treatment Structure. 8.10 Make Hierarchical Analyses the Default Analysis. 8.11 Distinguish Between Nested and Crossed Designs-Not Always Easy. 8.12 Plan for Missing Data. 8.13 Address Multiple Comparisons Before Starting the Study. 8.14 Know Properties Preserved When Transforming Units. 8.15 Consider Bootstrapping for Complex Relationships. 9. Words, Tables, and Graphs. 9.1 Use Text for a Few Numbers, Tables for Many Numbers, Graphs and Complex Relationships. 9.2 Arrange Information in a Table to Drive Home the Message. 9.3 Always Graph the Data. 9.4 Always Graph Results of An Analysis of Variance. 9.5 Never Use a Pie Chart. 9.6 Bar Graphs Waste Ink; They Don’t Illuminate Complex Relationships. 9.7 Stacked Bar Graphs Are Worse Than Bar Graphs. 9.8 Three-Dimensional Bar Graphs Constitute Misdirected Artistry. 9.9 Identify Cross-sectional and Longitudinal Patterns in Longitudinal Data. 9.10 Use Rendering, Manipulation, and Linking in High-Dimensional Data. 10. Consulting. 10.1 Session Has Beginning, Middle, and End. 10.2 Ask Questions. 10.3 Make Distinctions. 10.4 Know Yourself, Know the Investigator. 10.5 Tailor Advice to the Level of the Investigator. 10.6 Use Units the Investigator is Comfortable With. 10.7 Agee on Assignment of Responsibilities. 10.8 Any Basic Statistical Computing Package Will Do. 10.9 Ethics Precedes, Guides, and Follows Consultation. 10.10 Be Proactive in Statistical Consulting. 10.11 Use the Web for Reference, Resource, and Education. 10.12 Listen to, and Heed the Advice of Experts in the Field. Epilogue. Reference. Author Index. Topic Index.

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Book SynopsisParameter Estimation for Scientists and Engineers discusses estimating parameters of expectation models of statistical observations. It aims to show scientists and engineers, who often are not aware of estimators other than least squares, that statistical parameter estimation has much more to offer than least squares estimation alone.Trade Review“An indispensable tool for scholars and research workers in mathematics and the mathematical sciences.” (Mathematical Reviews, 2009) "Despite its lean size, the book is able to cover many of the techniques and theories in parameter estimation that are core to applied sciences, and so this is certainly a valuable reference for researchers and graduate students alike. The book's exposition is lucid, making it an accessible reading for someone with a reasonable background in elementary statistics. Thus I think anyone in applied sciences and engineering dealing with the implementation of expectation models and aiming to estimate model parameters will find this book helpful. This is a great addition to resources in learning or reviewing statistical tools that emphasize taking advantage of valuable information from data and improving the precision of estimation." (Technometrics, November 2008) "I highly recommend this book to practitioners who want to systematically learn and use, new, better techniques for parameter estimation." (Computing Reviews, September 10, 2008) "…appropriate for students in advanced applied statistics courses…even more useful as a supplemental resource…" (CHOICE, January 2008)Table of ContentsPreface. 1 Introduction. 2 Parametric Models of Observations. 3 Distributions of Observations. 4 Precision and Accuracy. 5 Precise and Accurate Estimation. 6 Numerical Methods for Parameter Estimation. 7 Solutions or Partial Solutions to Problems. Appendix A: Statistical Results. Appendix B: Vectors and Matrices. Appendix C: Positive Semidefinite and Positive Definite Matrices. Appendix D: Vector and Matrix Differentiation. References. Topic Index.

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