Probability and statistics Books

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Book SynopsisThis book offers an easily accessible and comprehensive guide to the entire market research process, from asking market research questions to collecting and analyzing data by means of quantitative methods. It is intended for all readers who wish to know more about the market research process, data management, and the most commonly used methods in market research. The book helps readers perform analyses, interpret the results, and make sound statistical decisions using IBM SPSS Statistics. Hypothesis tests, ANOVA, regression analysis, principal component analysis, factor analysis, and cluster analysis, as well as essential descriptive statistics, are covered in detail. Highly engaging and hands-on, the book includes many practical examples, tips, and suggestions that help readers apply and interpret the data analysis methods discussed. The new edition uses IBM SPSS version 25 and offers the following new features:A single case and dataset used throughout the book to facilitate learningNew material on survey design and all data analysis methods to reflect the latest advances concerning each topic Improved use of educational elements, such as learning objectives, keywords, self-assessment tests, case studies, and much more A glossary that includes definitions of all the keywords and other descriptions of selected topics Links to additional material and videos via the Springer Multimedia App Table of ContentsIntroduction to Market Reseach.- The Market Research Process.- Data.- Getting Data.- Descriptive Statistics.- Hypothesis Testing & ANOVA.- Regression Analysis.- Principal Component and Factor Analysis.-Cluster Analysis.- Communicating the Results.

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Book SynopsisThis book includes a novel motif discovery for time series, KITE (ill-Known motIf discovery in Time sEries data), to identify ill-known motifs transformed by affine mappings such as translation, uniform scaling, reflection, stretch, and squeeze mappings. Additionally, such motifs may be covered with noise or have variable lengths. Besides KITE’s contribution to motif discovery, new avenues for the signal and image processing domains are explored and created. The core of KITE is an invariant representation method called Analytic Complex Quad Tree Wavelet Packet transform (ACQTWP). This wavelet transform applies to motif discovery as well as to several signal and image processing tasks. The efficiency of KITE is demonstrated with data sets from various domains and compared with state-of-the-art algorithms, where KITE yields the best outcomes.Trade Review“The book under review provides one such vantage point, and anyone whose work involves finding patterns in large amounts of data should take heed. … For those well versed in the mathematics of harmonics and waves, the book should prove very useful in showing how these theories can be applied to data series. But even those who are not specialists in this area, such as myself, can still gain many ideas from this useful tome.” (Eugene Callahan, Computing Reviews, October 11, 2022)Table of ContentsIntroduction.- Preliminaries.- General Principles of Time Series Motif Discovery.- State of the Art in Time Series Motif Discovery.- Distortion-Invariant Motif Discovery.- Evaluation.- Conclusion and Outlook.- Appendices A-D.

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Book SynopsisThis book provides advanced theoretical and applied tools for the implementation of modern micro-econometric techniques in evidence-based program evaluation for the social sciences. The author presents a comprehensive toolbox for designing rigorous and effective ex-post program evaluation using the statistical software package Stata. For each method, a statistical presentation is developed, followed by a practical estimation of the treatment effects. By using both real and simulated data, readers will become familiar with evaluation techniques, such as regression-adjustment, matching, difference-in-differences, instrumental-variables, regression-discontinuity-design, and synthetic control method, and are given practical guidelines for selecting and applying suitable methods for specific policy contexts.The second revised and extended edition features two new chapters on some recent development of difference-in-differences. Specifically, chapter 5 introduces advanced difference-in-differences methods when many times are available and treatment can be either time-varying or fixed at a specific time. Chapter 6 introduces the synthetic control method, a treatment effect estimation approach suitable when only one unit is treated. Both chapters present applications using the software Stata.Table of ContentsChapter 1. An Introduction to the Econometrics of Program Evaluation.- Chapter 2. Methods Based on Selection on Observables.- Chapter 3. Methods Based on Selection on Unobservables.- Chapter 4. Local Average Treatment Effect and Regression-Discontinuity-Design.- Chapter 5. Difference-in-differences with many pre- and post-treatment times.- Chapter 6. Synthetic Control Method

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Book SynopsisThis book offers a systematic introduction to the optimal stochastic control theory via the dynamic programming principle, which is a powerful tool to analyze control problems.First we consider completely observable control problems with finite horizons. Using a time discretization we construct a nonlinear semigroup related to the dynamic programming principle (DPP), whose generator provides the Hamilton–Jacobi–Bellman (HJB) equation, and we characterize the value function via the nonlinear semigroup, besides the viscosity solution theory. When we control not only the dynamics of a system but also the terminal time of its evolution, control-stopping problems arise. This problem is treated in the same frameworks, via the nonlinear semigroup. Its results are applicable to the American option price problem.Zero-sum two-player time-homogeneous stochastic differential games and viscosity solutions of the Isaacs equations arising from such games are studied via a nonlinear semigroup related to DPP (the min-max principle, to be precise). Using semi-discretization arguments, we construct the nonlinear semigroups whose generators provide lower and upper Isaacs equations.Concerning partially observable control problems, we refer to stochastic parabolic equations driven by colored Wiener noises, in particular, the Zakai equation. The existence and uniqueness of solutions and regularities as well as Itô's formula are stated. A control problem for the Zakai equations has a nonlinear semigroup whose generator provides the HJB equation on a Banach space. The value function turns out to be a unique viscosity solution for the HJB equation under mild conditions.This edition provides a more generalized treatment of the topic than does the earlier book Lectures on Stochastic Control Theory (ISI Lecture Notes 9), where time-homogeneous cases are dealt with. Here, for finite time-horizon control problems, DPP was formulated as a one-parameter nonlinear semigroup, whose generator provides the HJB equation, by using a time-discretization method. The semigroup corresponds to the value function and is characterized as the envelope of Markovian transition semigroups of responses for constant control processes. Besides finite time-horizon controls, the book discusses control-stopping problems in the same frameworks.

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Book SynopsisThis study provides innovative mathematical models for assessing the eruption probability and associated volcanic hazards, and applies them to the Campi Flegrei caldera in Italy. Throughout the book, significant attention is devoted to quantifying the sources of uncertainty affecting the forecast estimates. The Campi Flegrei caldera is certainly one of the world’s highest-risk volcanoes, with more than 70 eruptions over the last 15,000 years, prevalently explosive ones of varying magnitude, intensity and vent location. In the second half of the twentieth century the volcano apparently once again entered a phase of unrest that continues to the present. Hundreds of thousands of people live inside the caldera and over a million more in the nearby city of Naples, making a future eruption of Campi Flegrei an event with potentially catastrophic consequences at the national and European levels.Table of ContentsIntroduction.- Vent opening probability maps.- Pyroclastic density current invasion maps.- Time-space model for the next eruption.- Addendum.- Supporting information.

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Book SynopsisThis book provides an inter-disciplinary introduction to the theory of random fields and its applications. Spatial models and spatial data analysis are integral parts of many scientific and engineering disciplines. Random fields provide a general theoretical framework for the development of spatial models and their applications in data analysis. The contents of the book include topics from classical statistics and random field theory (regression models, Gaussian random fields, stationarity, correlation functions) spatial statistics (variogram estimation, model inference, kriging-based prediction) and statistical physics (fractals, Ising model, simulated annealing, maximum entropy, functional integral representations, perturbation and variational methods). The book also explores links between random fields, Gaussian processes and neural networks used in machine learning. Connections with applied mathematics are highlighted by means of models based on stochastic partial differential equations. An interlude on autoregressive time series provides useful lower-dimensional analogies and a connection with the classical linear harmonic oscillator. Other chapters focus on non-Gaussian random fields and stochastic simulation methods. The book also presents results based on the author’s research on Spartan random fields that were inspired by statistical field theories originating in physics. The equivalence of the one-dimensional Spartan random field model with the classical, linear, damped harmonic oscillator driven by white noise is highlighted. Ideas with potentially significant computational gains for the processing of big spatial data are presented and discussed. The final chapter concludes with a description of the Karhunen-Loève expansion of the Spartan model. The book will appeal to engineers, physicists, and geoscientists whose research involves spatial models or spatial data analysis. Anyone with background in probability and statistics can read at least parts of the book. Some chapters will be easier to understand by readers familiar with differential equations and Fourier transforms.Trade Review“I would say … that the author’s use of an interdisciplinary approach in presenting the field of spatial data modeling is what makes this book truly unique. … I believe anyone who is willing to learn about and understand concepts, assumptions and methods behind spatial data modeling would benefit from having a copy of this outstanding book.” (Sandra De Iaco, Mathematical Geosciences, February 12, 2021)Table of ContentsIntroduction.- Preliminary Remarks.- Why Random Fields?.- Notation and Definitions.- Noise and Errors.- Spatial Data and Basic Processing Procedures.- A Personal Selection of Relevant Books.- Trend Models and Estimation.- Empirical Trend Estimation.- Regression Analysis.- Global Trend Models.- Local Trend Models.- Trend Estimation based on Physical Information.- Trend Based on the Laplace Equation.- Basic Notions of Random Fields.- Introduction.- Single-Point Description.- Stationarity and Statistical Homogeneity.- Variogram versus Covariance.- Permissibility of Covariance Functions.- Permissibility of Variogram Functions.- Additional Topics of Random Field Modeling.- Ergodicity.- Statistical Isotropy.- Anisotropy.- Anisotropic Spectral Densities.- Multipoint Description of Random Fields.- Geometric Properties of Random Fields.- Local Properties.- Covariance Hessian Identity and Geometric Anisotropy.- Spectral Moments.- Length Scales of Random Fields.- Fractal Dimension.- Long-Range Dependence.- Intrinsic Random Fields.- Fractional Brownian Motion.- Classification of Random Fields.- Gaussian Random Fields.- Multivariate Normal Distribution.- Field Integral Formulation.- Useful Properties of Gaussian Random Fields.- Perturbation Theory for Non-Gaussian Probability Densities.- Non-stationary Covariance Functions.- Further Reading.- Random Fields based on Local Interactions.- Spartan Spatial Random Fields.- Two-point Functions and Realizations.- Statistical and Geometric Properties.- Bessel-Lommel Covariance Functions.- Lattice Representations of Spartan Random Fields.- Introduction to Gauss-Markov Random Fields.- From Spartan Random Fields to Gauss-Markov Random Fields.- Lattice Spectral Density.- SSRF Lattice Moments.- SSRF Inverse Covariance Operator on Lattices.- Spartan Random Fields and Langevin Equations.- Introduction to Stochastic Differential Equations.- Classical Harmonic Oscillator.- Stochastic Partial Differential Equations.- Spartan Random Fields and Stochastic Partial Differential Equations.- Covariance and Green’s functions.- Whittle-Matérn Stochastic Partial Differential Equation.- Diversion in Time Series.- Spatial Prediction Fundamentals.- General Principles of Linear Prediction.- Deterministic Interpolation.- Stochastic Methods.- Simple Kriging.- Ordinary Kriging.- Properties of the Kriging Predictor.- Topics Related to the Application of Kriging.- Evaluating Model Performance.- More on Spatial Prediction.- Linear Generalizations of Kriging.- Nonlinear Extensions of Kriging.- Connections with Gaussian Process Regression.- Bayesian Kriging.- Continuum Formulation of Linear Prediction.- The “Local-Interaction” Approach.- Big Spatial Data.- Basic Concepts and Methods of Estimation.- Estimator Properties.- Estimating the Mean with Ordinary Kriging.- Variogram Estimation.- Maximum Likelihood Estimation.- Cross Validation.- More on Estimation.- The Method of Normalized Correlations.- The Method of Maximum Entropy.- Stochastic Local Interactions.- Measuring Ergodicity.- Beyond the Gaussian Models.- Trans-Gaussian Random Fields.- Gaussian Anamorphosis.- Tukey g-h Random Fields.- Transformations based on Kappa Exponentials.- Hermite Polynomials.- Multivariate Student’s t-distribution.- Copula Models.- The Replica Method.- Binary Random Fields.- The Indicator Random Field.- Ising Model.- Generalized Linear Models.- Simulations.- Introduction.- Covariance Matrix Factorization.- Spectral Simulation Methods.- Fast-Fourier-Transform Simulation.- Randomized Spectral Sampling.- Conditional Simulation based on Polarization Method.- Conditional Simulation based on Covariance Matrix Factorization.- Monte Carlo Methods.- Sequential Simulation of Random Fields.- Simulated Annealing.- Karhunen-Loève Expansion.- Karhunen-Loève Expansion of Spartan Random Fields.- Epilogue.- A Jacobi’s Transformation Theorems.- B Tables of SSRF Properties.- C Linear Algebra Facts.- D Kolmogorov-Smirnov Test.- Glossary.- References.- Index.

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Book SynopsisThis book provides a first introduction to the methods of probability theory by using the modern and rigorous techniques of measure theory and functional analysis. It is geared for undergraduate students, mainly in mathematics and physics majors, but also for students from other subject areas such as economics, finance and engineering. It is an invaluable source, either for a parallel use to a related lecture or for its own purpose of learning it.The first part of the book gives a basic introduction to probability theory. It explains the notions of random events and random variables, probability measures, expectation values, distributions, characteristic functions, independence of random variables, as well as different types of convergence and limit theorems. The first part contains two chapters. The first chapter presents combinatorial aspects of probability theory, and the second chapter delves into the actual introduction to probability theory, which contains the modern probability language. The second part is devoted to some more sophisticated methods such as conditional expectations, martingales and Markov chains. These notions will be fairly accessible after reading the first part. --

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Book SynopsisThis research monograph explores new frontiers in Markov chains. Although time-homogeneous Markov chains are well understood, this is not at all the case with time-inhomogeneous ones. The book, after a review on the classical theory of homogeneous chains, including the electrical network approach, introduces several new models which involve inhomogeneous chains as well as related new types of random walks (for example, 'coin turning', 'conservative' and 'Rademacher' walk). Scaling limits, the breakdown of the classical limit theorems as well as recurrence and transience are investigated. The relationship with urn models is the subject of two chapters, providing additional connections to other parts of probability theory.Random walks on random graphs are discussed as well, as an area where the method of electric networks is especially useful. This is illustrated by presenting random walks in random environments and random labyrinths.The monograph puts emphasis on showing examples and open problems besides providing rigorous analysis of the models.Several figures illustrate the main ideas, and a large number of exercises challenge the interested reader.

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Book SynopsisThis book seeks to bridge the gap between statistics and computer science. It provides an overview of Monte Carlo methods, including Sequential Monte Carlo, Markov Chain Monte Carlo, Metropolis-Hastings, Gibbs Sampler, Cluster Sampling, Data Driven MCMC, Stochastic Gradient descent, Langevin Monte Carlo, Hamiltonian Monte Carlo, and energy landscape mapping. Due to its comprehensive nature, the book is suitable for developing and teaching graduate courses on Monte Carlo methods. To facilitate learning, each chapter includes several representative application examples from various fields. The book pursues two main goals: (1) It introduces researchers to applying Monte Carlo methods to broader problems in areas such as Computer Vision, Computer Graphics, Machine Learning, Robotics, Artificial Intelligence, etc.; and (2) it makes it easier for scientists and engineers working in these areas to employ Monte Carlo methods to enhance their research.Trade Review“This monograph ... is intended to be a textbook for graduate students in statistics, computer science and engineering. It covers a very broad range of topics ... . Each chapter is finished by a rather long list of relevant references. Thus, it can be used also as a reference book by researches in the fields of machine learning, pattern recognition ... . it can be a useful reference to many important Monte Carol methods.” (Jaromír Antoch, zbMATH 1483.65001, 2022)“True to its goal, the text offers a comprehensive overview on Monte Carlo methods. … this text is a quality reference for researchers interested in computer vision, computer graphics, machine learning, artificial intelligence and related fields.” (Grant Innerst, MAA Reviews, July 18, 2021)Table of Contents1 Introduction to Monte Carlo Methods.- 2 Sequential Monte Carlo.- 3 Markov Chain Monte Carlo - the Basics.- 4 Metropolis Methods and Variants.- 5 Gibbs Sampler and its Variants.- 6 Cluster Sampling Methods.- 7 Convergence Analysis of MCMC.- 8 Data Driven Markov Chain Monte Carlo.- 9 Hamiltonian and Langevin Monte Carlo.- 10 Learning with Stochastic Gradient.- 11 Mapping the Energy Landscape.

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Book SynopsisThis book addresses sample size and power in the context of research, offering valuable insights for graduate and doctoral students as well as researchers in any discipline where data is generated to investigate research questions. It explains how to enhance the authenticity of research by estimating the sample size and reporting the power of the tests used. Further, it discusses the issue of sample size determination in survey studies as well as in hypothesis testing experiments so that readers can grasp the concept of statistical errors, minimum detectable difference, effect size, one-tail and two-tail tests and the power of the test. The book also highlights the importance of fixing these boundary conditions in enhancing the authenticity of research findings and improving the chances of research papers being accepted by respected journals. Further, it explores the significance of sample size by showing the power achieved in selected doctoral studies. Procedure has been discussed to fix power in the hypothesis testing experiment. One should usually have power at least 0.8 in the study because having power less than this will have the issue of practical significance of findings. If the power in any study is less than 0.5 then it would be better to test the hypothesis by tossing a coin instead of organizing the experiment. It also discusses determining sample size and power using the freeware G*Power software, based on twenty-one examples using different analyses, like t-test, parametric and non-parametric correlations, multivariate regression, logistic regression, independent and repeated measures ANOVA, mixed design, MANOVA and chi-square.Table of ContentsPreface Acknowledgements 1 Introduction to Sample Size Determination Introduction Issue of Power due to inappropriate sample size Some case studies Flow Diagram of Determining sample size and power Summary 2 Understanding Statistical Inference Introduction Estimating Parameters Estimating Population Mean Confidence Coefficient Confidence Interval Factors Affecting Confidence Interval Estimating Population Proportion Hypothesis Testing Type I and Type II Errors Power of the Test Relationship between Type I and Type II Errors One Tailed and Two Tailed Tests Procedure in Hypothesis Testing Experiment Effect Size Summary 3 Understanding Concepts in Estimating Sample Size in Survey Studies Introduction Determining Sample Size in Estimating Population Mean Factors Affecting Sample Size Sample Size Determination for Estimating Mean when Population SD Known: Illustration 3.1 Sample Size Determination for Estimating Mean when Population SD Unknown: Illustration 3.2 Sample Size Determination for Estimating Mean when Population SD Unknown: Illustration 3.3 Sample Size Determination for Estimating Mean when Population SD Unknown: Illustration 3.4 Determining Sample Size in Estimating Population Proportion Sample Size Determination for Estimating Proportion: Illustration 3.5 Sample Size Determination for Estimating Proportion: Illustration 3.6 Sample Size Determination for Estimating Proportion: Illustration 3.7 Sample Size Determination for Estimating Proportion: Illustration 3.8 Determining Sample Size in Estimating Difference Between Two Population Means Summary 4 Understanding Concepts in Estimating Sample Size in Hypothesis Testing Experiment Introduction Sample Size on the Basis of Power One Sample Testing of Mean Determining Sample Size Estimation of Minimum Sample Size to Test H0 : µ=37 : Illustration 4.1 Minimum Detectable Difference Estimation of Minimum Detectable Difference for Testing H0: µ=37: Illustration 4.2 Estimation of Power in One Sample t Test Estimation of Power in Testing H0: µ=37: Illustration 4.3 Testing Difference Between Two Means Determining Sample Size in Two Sample t Test Estimation of Sample Size for Two Sample t Test for Mean : Illustration 4.4 Estimation of Power in Two Sample t Test Estimation of Power in Two Sample t Test for Mean : Illustration 4.5 Summary 5 Use of G*Power Software Introduction Procedure of Installing G*Power 3.1 Summary 6 Determining Sample Size in Experimental Studies Introduction One Sample Testing Testing Difference of Sample Mean from Population Mean Sample Size and Power Determination: Illustration 6.1 Testing Difference of Sample Proportion from Population Proportion Sample Size Determination: Illustration 6.2 Two Sample Testing Comparing Group Means in Two Independent Samples Sample Size and Power Determination: Illustration 6.3 Comparing Paired Group Means Sample Size Determination: Illustration 6.4 Comparing two Group Means Using Mann Whitney Test Sample Size Determination: Illustration 6.5 Comparing Paired Group Means Using Wilcoxon Signed Rank Test Sample Size Determination: Illustration 6.6 Comparing Two Proportions Sample Size Determination: Illustration 6.7 Correlation Coefficient: Testing Significance Case I: Testing Whether Sample Correlation Differs From 0 Sample Size Determination: Illustration 6.14 Case II: Testing Whether Sample Correlation Differs from a Known Value Sample Size Determination: Illustration 6.15 Correlation Coefficients: Testing Significant Difference Between Two Independent Correlations Sample Size Determination: Illustration 6.16 Bi-Serial Correlation: Testing Significance Sample Size Determination: Illustration 6.17 Goodness of Fit: Testing With Chi-Square Sample Size Determination in Goodness of Fit: Illustration 6.18 Linear Multiple Regression Model Sample Size Determination in Linear Multiple Regression: Illustration 6.19 Logistic Regression Sample Size Determination for Continuous Predictors: Illustration 6.20 Sample Size Determination for a Dichotomous Predictor: Illustration 6.21 Summary 7 Determining Sample Size in General Linear Models Introduction Analysis of Variance One–Way Analysis of Variance Sample Size Determination: Illustration 6.8 Two–Way Analysis of Variance Sample Size Determination for Main and Interaction Effect: Illustration 6.9 Repeated Measures ANOVA Between Factors Sample Size Determination: Illustration 6.10 Repeated Measures ANOVA Within Factors Sample Size Determination: Illustration 6.11 Repeated ANOVA Within-Between Interaction Manova Experiment: for Testing the Significance of Global Effect Sample Size Determination: Illustration 6.12 Manova Experiment: Testing Significance of Interaction Effect Sample Size Determination: Illustration 6.13 Summary Appendix Bibliography

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Book SynopsisIn China, lots of excellent students who are good at maths take an active part in various maths contests and the best six senior high school students will be selected to form the IMO National Team to compete in the International Mathematical Olympiad. In the past ten years China's IMO Team has achieved outstanding results — they have won the first place almost every year.The author is one of the senior coaches of China's IMO National Team, whose students have won many gold medals many times in IMO.This book is part of the Mathematical Olympiad Series which discusses several aspects related to maths contests, such as algebra, number theory, combinatorics, graph theory and geometry. This book will, in an interesting problem-solving way, explain what probability theory is: its concepts, methods and meanings; particularly, two important concepts — probability and mathematical expectation (briefly expectation) — are emphasized. It consists of 65 problems, appended by 107 exercises and their answers.

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Book SynopsisThis is an essential textbook for senior undergraduate and graduate students of statistics, stochastic processes, stochastic finance, and probability theory. It thoroughly discusses the concepts of stochastic processes, both Markov and non-Markov processes, as well as stochastic calculus.

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Book SynopsisBy means of a series of exchanges between the editors and leaders from the philosophy of science, statistics and economics, this volume offers a cumulative introduction connecting problems of traditional philosophy of science to problems of inference in statistical and empirical modelling practice.Trade Review'Mayo and Spanos's collection has injected new ideas into the study of scientific inference. This book offers a welcome bridge between current philosophy of science and scientific practice, providing the reader with new insights on important topics such as statistical inference, reliability, theory testing, causal modeling, and the relation between theory and experiment. The book will have a wide and enthusiastic readership among philosophers and scientists.' Cristina Bicchieri, University of Pennsylvania'Error and Inference straddles philosophy and practice; its lessons should be taken seriously in both. The editors suppose that venerable philosophical problems surrounding induction, scientific inference, and objectivity can be solved. The essays in the book give support to that perspective. They also show that pressing practical problems of scientific inference and testing gain marked benefit from careful attention to philosophers' accounts of what makes for evidence, rationality, and objectivity.' Nancy Cartwright, London School of Economics'The error-probabilistic approach developed by Deborah Mayo and Aris Spanos is the main alternative to Bayesianism in contemporary philosophy of science. In this superb volume Mayo and Spanos face their critics and show that error-probabilism is able to solve most theoretical puzzles of statistical testing. If some issue in the field of inductive inference is bothering you, you will probably find an answer in this book.' Francesco Guala, University of Milan'Mayo, an empirically minded philosopher, and Spanos, a philosophically minded economist, have succeeded beautifully in orchestrating a lively debate over methodological issues related to statistics and empirical testing that - unlike too much of the philosophy of science - speaks to the genuine issues that the practitioners of empirical sciences face daily. Their important volume deserves a broad readership.' Kevin Hoover, Duke University'Mayo and Spanos continue their campaign to bring confirmation theory face-to-face with the methods of scientists, and now extend it to the history of science and to general theories too. This book begins with a fine introduction to Mayo's error-statistical approach that makes the book a useful teaching tool. But then it carries forward the discussion of this approach with challenging papers from Glymour, Laudan, Achinstein, Worrall, and others.' Alexander Rosenberg, Duke University'This is a wonderful volume. It contains original and stimulating essays by leading figures from both philosophy and statistics on notions of evidence and testing; on how these interact with ideas about causation, explanation, and scientific rationality; and much more besides. The volume also features detailed and illuminating exchanges between the contributors. A must-read for anyone with an interest in these topics.' Jim Woodward, California Institute of TechnologyTable of ContentsPart I. Introduction and Background: 1. Philosophy of methodological practice Deborah Mayo; 2. Error statistical philosophy Deborah Mayo and Aris Spanos; Part II: 3. Severe testing, error statistics, and the growth of theoretical knowledge Deborah Mayo; Part III: 4. Can scientific theories be warranted? Alan Chalmers; 5. Can scientific theories be warranted with severity? Exchanges with Alan Chalmers Deborah Mayo; Part IV: 6. Critical rationalism, explanation and severe tests Alan Musgrave; 7. Towards progressive critical rationalism: exchanges with Alan Musgrave Deborah Mayo; Part V: 8. Error, tests and theory-confirmation John Worrall; 9. Has Worrall saved his theory (on ad hoc saves) in a non ad hoc manner? Exchanges with Worrall Deborah Mayo; Part VI: 10. Mill's sins, or Mayo's errors? Peter Achinstein; 11. Sins of the Bayesian epistemologist: exchanges with Achinstein Deborah Mayo; Part VII: 12. Theory testing in economics and the error statistical perspective Aris Spanos; Part VIII: 13. Frequentist statistics as a theory of inductive inference Deborah Mayo and David Cox; 14. Objectivity and conditionality in Frequentist inference David Cox and Deborah Mayo; 15. An error in the argument from WCP and S to the SLP Deborah Mayo; 16. On a new philosophy of Frequentist inference: exchanges with Cox and Mayo Aris Spanos; Part IX: 17. Explanation and truth Clark Glymour; 18. Explanation and testing: exchanges with Glymour Deborah Mayo; 19. Graphical causal modeling and error statistics: exchanges with Glymour Aris Spanos; Part X: 20. Legal epistemology: the anomaly of affirmative defenses Larry Laudan; 21. Error and the law: exchanges with Laudan Deborah Mayo.

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Book SynopsisExplores an important aspect of number theory - the theory of exponential sums over finite fields and their Mellin transforms - from a categorical point of view. This book presents fundamentally important results and a plethora of examples, opening up new directions in the subject.Trade Review"The book is written in a clear and enlightening style. The author provides the reader with many examples that are developed throughout a dozen chapters. These examples help understand and clarify the depth and the variety of applications of the beautiful main equidistribution statement that relies on rather complicated and subtle algebrageometric arguments."--Florent Jouve, Mathematical Reviews Clippings "The book provides the reader with much material around the question of the equidistribution of the angles if one fixes f and varies over the multiplicative character x. More than one hundred pages of examples provide the reader with great insight in the different applications of the main theorem. This turns the book into a very good basis for research in this area."--Manfred G. Madritsch, Zentralblatt MATH "Once a certain basic understanding is reached, this book, like the others written by N. Katz, reveals itself to be very precisely and sharply written, and to be full of riches. And finally, this theory shows spectacularly how some of the most abstract ideas of algebra and algebraic geometry may be essential to solving extremely concrete problems."--Emmanuel Kowalski, Bulletin of the American Mathematical SocietyTable of Contents*FrontMatter, pg. i*Contents, pg. vi*Introduction, pg. 1*CHAPTER 1. Overview, pg. 7*CHAPTER 2. Convolution of Perverse Sheaves, pg. 19*CHAPTER 3. Fibre Functors, pg. 21*CHAPTER 4. The Situation over a Finite Field, pg. 25*CHAPTER 5. Frobenius Conjugacy Classes, pg. 31*CHAPTER 6. Group-Theoretic Facts about Ggeom and Garith, pg. 33*CHAPTER 7. The Main Theorem, pg. 39*CHAPTER 8. Isogenies, Connectedness, and Lie-Irreducibility, pg. 45*CHAPTER 9. Autodualities and Signs, pg. 49*CHAPTER 10. A First Construction of Autodual Objects, pg. 53*CHAPTER 11. A Second Construction of Autodual Objects, pg. 55*CHAPTER 12. The Previous Construction in the Nonsplit Case, pg. 61*CHAPTER 13. Results of Goursat-Kolchin-Ribet Type, pg. 63*CHAPTER 14. The Case of SL(2); the Examples of Evans and Rudnick, pg. 67*CHAPTER 15. Further SL(2) Examples, Based on the Legendre Family, pg. 73*CHAPTER 16. Frobenius Tori and Weights; Getting Elements of Garith, pg. 77*CHAPTER 17. GL(n) Examples, pg. 81*CHAPTER 18. Symplectic Examples, pg. 89*CHAPTER 19. Orthogonal Examples, Especially SO(n) Examples, pg. 103*CHAPTER 20. GL(n) x GL(n) x ... x GL(n) Examples, pg. 113*CHAPTER 21. SL(n) Examples, for n an Odd Prime, pg. 125*CHAPTER 22. SL(n) Examples with Slightly Composite n, pg. 135*CHAPTER 23. Other SL(n) Examples, pg. 141*CHAPTER 24. An O(2n) Example, pg. 145*CHAPTER 25. G2 Examples: the Overall Strategy, pg. 147*CHAPTER 26. G2 Examples: Construction in Characteristic Two, pg. 155*CHAPTER 27. G2 Examples: Construction in Odd Characteristic, pg. 163*CHAPTER 28. The Situation over Z: Results, pg. 173*CHAPTER 29. The Situation over Z: Questions, pg. 181*CHAPTER 30. Appendix: Deligne's Fibre Functor, pg. 187*Bibliography, pg. 193*Index, pg. 197

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Book SynopsisAn Introduction to Statistical Learning provides an accessible overview of the field of statistical learning, an essential toolset for making sense of the vast and complex data sets that have emerged in fields ranging from biology to finance to marketing to astrophysics in the past twenty years. This book presents some of the most important modeling and prediction techniques, along with relevant applications. Topics include linear regression, classification, resampling methods, shrinkage approaches, tree-based methods, support vector machines, clustering, deep learning, survival analysis, multiple testing, and more. Color graphics and real-world examples are used to illustrate the methods presented. Since the goal of this textbook is to facilitate the use of these statistical learning techniques by practitioners in science, industry, and other fields, each chapter contains a tutorial on implementing the analyses and methods presented in R, an extremely popular open source statistical sTable of ContentsPreface.- 1 Introduction.- 2 Statistical Learning.- 3 Linear Regression.- 4 Classification.- 5 Resampling Methods.- 6 Linear Model Selection and Regularization.- 7 Moving Beyond Linearity.- 8 Tree-Based Methods.- 9 Support Vector Machines.- 10 Deep Learning.- 11 Survival Analysis and Censored Data.- 12 Unsupervised Learning.- 13 Multiple Testing.- Index.

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Book SynopsisFrom the reviews: Paul Glasserman has written an astonishingly good book that bridges financial engineering and the Monte Carlo method. The book will appeal to graduate students, researchers, and most of all, practicing financial engineers [...] So often, financial engineering texts are very theoretical. This book is not. --Glyn Holton, Contingency AnalysisTrade Review"Paul Glasserman has written an astonishingly good book that bridges financial engineering and the Monte Carlo method. The book will appeal to graduate students, researchers, and most of all, practicing financial engineers … You will want to have prior knowledge of both the Monte Carlo method and financial engineering. If you do, you will find the book to be a goldmine … So often, financial engineering texts are very theoretical. This book is not. The Monte Carlo method serves as a unifying theme that motivates practical discussions of how to implement real models on real trading floors. You will learn plenty of financial engineering amidst these pages. The writing is a pleasure to read. Topics are timely and relevant. Glasserman's is a must-have book for financial engineers." -Glyn Holton, Contingency AnalysisMathematical Reviews, 2004: "... this book is very comprehensive, up-to-date and useful tool for those who are interested in implementing Monte Carlo methods in a financial context." From the reviews: "This recent book is a valuable addition to the references devoted to Monte Carlo methods. … the author succeeded in choosing the most actual topics in financial engineering and in presenting them in an appropriate way by keeping a suitable balance between mathematical rigour and an audience friendly language. … To help the reader, three appendices provide basic results on convergence concepts … . A large bibliography of 358 entries accompanies this text. In short, the reader will find this book extremely lucid and useful." (Radu Theodorescu, Zentralblatt MATH, Vol. 1038 (13), 2004) "To keep it short, let me summarize the recension in one phrase: Paul Glausserman’s book is a ‘strong buy’ for everybody in the financial community. … one gets 596 pages full of valuable information on all aspects of Monte Carlo simulation. … Altogether, I can encourage everyone interested in Monte Carlo methods in finance to read the book. It is very well written … comes with a carefully selected bibliography (358 references) and a helpful index, thus making it really worth the buy." (Ralf Werner, OR – Spectrum Operations Research Spectrum, Issue 27, 2005) "Glasserman’s new book is a remarkable presentation of the current state of the art of Monte Carlo Methods in Financial Engineering. … lot of material which is sometimes hard to access has been composed into one volume. … a high quality monograph which is both suitable as a reference for practitioners and researchers as well as a textbook … . The list of references is by itself a valuable aspect. The refreshing writing style of the author is tailor-made for the thirsty reader … ." (Uwe Wystup, www.mathfinance.de, November, 2003) "Paul Glasserman has written an astonishingly good book that bridges financial engineering and the Monte Carlo method. The book will appeal to graduate students, researchers, and most of all, practicing financial engineers. It is an advanced book. … The presentation is masterful. … You will learn plenty of financial engineering amidst the pages. The writing is a pleasure to read. Topics are timely and relevant. Glasserman’s is a must-have book for financial engineers." (www.riskbook.com, Dezember, 2003) "This book is divided into three parts. … the aim of the author is … to give a precise description of the different techniques in order to facilitate their implementation. In my opinion, this book is a very comprehensive, up-to-date and useful tool for those who are interested in implementing Monte Carlo methods in a financial context." (Benjamin Jourdain, Mathematical Reviews, 2004g) "The publication of this book is an important event in computational finance. For many years, Monte Carlo methods have been successfully applied to solve diverse problems in financial mathematics. By publishing this book the author deserves much credit for a very good attempt to lift such applications to a new level. … the book may well become a major reference in the field of applications of Monte Carlo methods in financial engineering. This is because the book is well structured and well written … ." (A Zhigljavsky, Journal of the Operational Research Society, Vol. 57, 2006)Table of ContentsFoundations.- Generating Random Numbers and Random Variables.- Generating Sample Paths.- Variance Reduction Techniques.- Quasi-Monte Carlo Methods.- Discretization Methods.- Estimating Sensitivities.- Pricing American Options.- Applications in Risk Management.- Appendices

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Book SynopsisGet going with tidymodels, a collection of R packages for modeling and machine learning. Whether you're just starting out or have years of experience with modeling, this practical introduction shows data analysts, business analysts, and data scientists how the tidymodels framework offers a consistent, flexible approach for your work.

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Book SynopsisThis book introduces machine learning methods in finance. It presents a unified treatment of machine learning and various statistical and computational disciplines in quantitative finance, such as financial econometrics and discrete time stochastic control, with an emphasis on how theory and hypothesis tests inform the choice of algorithm for financial data modeling and decision making. With the trend towards increasing computational resources and larger datasets, machine learning has grown into an important skillset for the finance industry. This book is written for advanced graduate students and academics in financial econometrics, mathematical finance and applied statistics, in addition to quants and data scientists in the field of quantitative finance. Machine Learning in Finance: From Theory to Practice is divided into three parts, each part covering theory and applications. The first presents supervised learning for cross-sectional data from both a Bayesian and frequentist perspective. The more advanced material places a firm emphasis on neural networks, including deep learning, as well as Gaussian processes, with examples in investment management and derivative modeling. The second part presents supervised learning for time series data, arguably the most common data type used in finance with examples in trading, stochastic volatility and fixed income modeling. Finally, the third part presents reinforcement learning and its applications in trading, investment and wealth management. Python code examples are provided to support the readers' understanding of the methodologies and applications. The book also includes more than 80 mathematical and programming exercises, with worked solutions available to instructors. As a bridge to research in this emergent field, the final chapter presents the frontiers of machine learning in finance from a researcher's perspective, highlighting how many well-known concepts in statistical physics are likely to emerge as important methodologies for machine learning in finance.Trade Review“This book is, however, a well-structured and self-contained graduate textbook on ML applications in finance. Exercises and some applications are included at the end of each chapter and the Python code used in this book makes use of the Python Tensor Flow library. This book could also serve as a useful reference book for researchers and practitioners in quantitative finance.” (Gilles Teyssière, Mathematical Reviews, February, 2023)“Each part is introduced with background information, examples of relevant practical applications, and references to the most recent scientific literature. … The book covers all essential areas of machine learning with relevance to quantitative finance. … An additional strong advantage of this book is the clear and consistent structure of its chapters. … Overall, the book covers multiple machine learning approaches with advanced technical exposition and is therefore especially suitable as an academic reference point, especially on Reinforcement Learning.” (Antoniya Shivarova, Financial Markets and Portfolio Management, Issue 35, 2021)“This volume aims to present a broad yet technical treatment of (ML) algorithms used by financial practitioners and scholars alike. … the book fills a large void. … This encourages reproducibility as well as learning by doing, which is highly appreciated.” (Guillaume Coqueret, Quantitative Finance, October 15, 2020)Table of ContentsChapter 1. Introduction.- Chapter 2. Probabilistic Modeling.- Chapter 3. Bayesian Regression & Gaussian Processes.- Chapter 4. Feed Forward Neural Networks.- Chapter 5. Interpretability.- Chapter 6. Sequence Modeling.- Chapter 7. Probabilistic Sequence Modeling.- Chapter 8. Advanced Neural Networks.- Chapter 9. Introduction to Reinforcement learning.- Chapter 10. Applications of Reinforcement Learning.- Chapter 11. Inverse Reinforcement Learning and Imitation Learning.- Chapter 12. Frontiers of Machine Learning and Finance.

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Book SynopsisThis textbook introduces the use of Python programming for exploring and modelling data in the field of Earth Sciences. It drives the reader from his very first steps with Python, like setting up the environment and starting writing the first lines of codes, to proficient use in visualizing, analyzing, and modelling data in the field of Earth Science. Each chapter contains explicative examples of code, and each script is commented in detail. The book is minded for very beginners in Python programming, and it can be used in teaching courses at master or PhD levels. Also, Early careers and experienced researchers who would like to start learning Python programming for the solution of geological problems will benefit the reading of the book.Table of ContentsPart I Python for Geologists, a kick-off; 1. Setting Up Your Python Environment, Easily; 2. Python Essentials for a Geologist; 3. Start Solving Geological Problems Using Python; Part II Describing Geological Data; 4. Graphical Visualization of a Geological Dataset; 5. Descriptive Statistics; Part III Integrals and Differential Equations in Geology; 6. Numerical Integration; 7. Ordinary Differential Equations (ODE); 8. Partial Differential Equations (PDE); Part IV Probability Density Functions and Error Analysis; 9. Probability Density Functions and their Use in Geology; 10. Error Analysis; Part V Robust Statistics and Machine Learning; 11. Introduction to Robust Statistics; 12. Machine Learning;

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Book SynopsisThis contributed volume convenes a rich selection of works with a focus on innovative mathematical methods with applications in real-world, industrial problems. Studies included in this book are all motivated by a relevant industrial challenge, and demonstrate that mathematics for industry can be extremely rewarding, leading to new mathematical methods and sometimes even to entirely new fields within mathematics.The book is organized into two parts: Computational Sciences and Engineering, and Data Analysis and Finance. In every chapter, readers will find a brief description of why such work fits into this volume; an explanation on which industrial challenges have been instrumental for their inspiration; and which methods have been developed as a result. All these contribute to a greater unity of the text, benefiting not only practitioners and professionals seeking information on novel techniques but also graduate students in applied mathematics, engineering, and related fields.Table of ContentsPart I: Computational Science and Engineering.- Multirate Schemes — An Answer of Numerical Analysis to a Demand from Applications.- Electronic Circuit Simulation and the Development of New Krylov-Subspace Methods.- Modular time integration of coupled problems in system dynamics.- Differential-Algebraic Equations and Beyond: From Smooth to Nonsmooth Constrained Dynamical Systems.- Fast Numerical Methods to Compute Periodic Solutions of Electromagnetic Models.- Challenges in the Simulation of Radio Frequency Circuits.- An integrated data-driven computational pipeline with model order reduction for industrial and applied mathematics.- From rotating fluid masses and Ziegler’s paradox to Pontryagin- and Krein spaces and bifurcation theory.- Part II: Data Analysis and finance.- Topological Data Analysis.- Prediction Models with Functional Data for Variables related with Energy Production.- Quantization Methods for Stochastic Differential Equations.

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Book SynopsisCluster analysis finds groups in data automatically. Most methods have been heuristic and leave open such central questions as: how many clusters are there? Which method should I use? How should I handle outliers? Classification assigns new observations to groups given previously classified observations, and also has open questions about parameter tuning, robustness and uncertainty assessment. This book frames cluster analysis and classification in terms of statistical models, thus yielding principled estimation, testing and prediction methods, and sound answers to the central questions. It builds the basic ideas in an accessible but rigorous way, with extensive data examples and R code; describes modern approaches to high-dimensional data and networks; and explains such recent advances as Bayesian regularization, non-Gaussian model-based clustering, cluster merging, variable selection, semi-supervised and robust classification, clustering of functional data, text and images, and co-clTrade Review'Bouveyron, Celeux, Murphy, and Raftery pioneered the theory, computation, and application of modern model-based clustering and discriminant analysis. Here they have produced an exhaustive yet accessible text, covering both the field's state of the art as well as its intellectual development. The authors develop a unified vision of cluster analysis, rooted in the theory and computation of mixture models. Embedded R code points the way for applied readers, while graphical displays develop intuition about both model construction and the critical but often-neglected estimation process. Building on a series of running examples, the authors gradually and methodically extend their core insights into a variety of exciting data structures, including networks and functional data. This text will serve as a backbone for graduate study as well as an important reference for applied data scientists interested in working with cutting-edge tools in semi- and unsupervised machine learning.' John S. Ahlquist, University of California, San Diego'This book, written by authoritative experts in the field, gives a comprehensive and thorough introduction to model-based clustering and classification. The authors not only explain the statistical theory and methods, but also provide hands-on applications illustrating their use with the open-source statistical software R. The book also covers recent advances made for specific data structures (e.g. network data) or modeling strategies (e.g. variable selection techniques), making it a fantastic resource as an overview of the state of the field today.' Bettina Grün, Johannes Kepler Universität Linz, Austria'Four authors with diverse strengths nicely integrate their specialties to illustrate how clustering and classification methods are implemented in a wide selection of real-world applications. Their inclusion of how to use available software is an added benefit for students. The book covers foundations, challenging aspects, and some essential details of applications of clustering and classification. It is a fun and informative read!' Naisyin Wang, University of Michigan'This is a beautifully written book on a topic of fundamental importance in modern statistical science, by some of the leading researchers in the field. It is particularly effective in being an applied presentation - the reader will learn how to work with real data and at the same time clearly presenting the underlying statistical thinking. Fundamental statistical issues like model and variable selection are clearly covered as well as crucial issues in applied work such as outliers and ordinal data. The R code and graphics are particularly effective. The R code is there so you know how to do things, but it is presented in a way that does not disrupt the underlying narrative. This is not easy to do. The graphics are 'sophisticatedly simple' in that they convey complex messages without being too complex. For me, this is a 'must have' book.' Rob McCulloch, Arizona State University'This advanced text explains the underlying concepts clearly and is strong on theory … I congratulate the authors on the theoretical aspects of their book, it's a fine achievement.' Antony Unwin, International Statistical Review'In my opinion, the overall quality of this impactful and intriguing book can be expressed by concluding that it is a perfect fit to the Cambridge Series in Statistical and Probabilistic Mathematics, characterized as a series of high-quality upper-division textbooks and expository monographs containing applications and discussions of new techniques while emphasizing rigorous treatment of theoretical methods.' Zdenek Hlavka, MathSciNet'… this book not only gives the big picture of the analysis of clustering and classification but also explains recent methodological advances. Extensive real-world data examples and R code for many methods are also well summarized. This book is highly recommended to students in data science, as well as researchers and data analysts.' Li-Pang Chen, Biometrical Journal'Model-Based Clustering and Classification for Data Science: With Applications in R, written by leading statisticians in the field, provides academics and practitioners with a solid theoretical and practical foundation on the use of model-based clustering methods … this book will serve as an excellent resource for quantitative practitioners and theoreticians seeking to learn the current state of the field.' C. M. Foley, Quarterly Review of Biology'This book frames cluster analysis and classification in terms of statistical models, thus yielding principled estimation, testing and prediction methods, and sound answers to the central questions … Written for advanced undergraduates in data science, as well as researchers and practitioners, it assumes basic knowledge of multivariate calculus, linear algebra, probability and statistics.' Hans-Jürgen Schmidt, zbMATHTable of Contents1. Introduction; 2. Model-based clustering: basic ideas; 3. Dealing with difficulties; 4. Model-based classification; 5. Semi-supervised clustering and classification; 6. Discrete data clustering; 7. Variable selection; 8. High-dimensional data; 9. Non-Gaussian model-based clustering; 10. Network data; 11. Model-based clustering with covariates; 12. Other topics; List of R packages; Bibliography; Index.

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Book SynopsisProvides a humorous tour through modern statistics as it is practiced in a wide variety of fields - from the humanities to the sciences. The book begins with a brief history of the subject, then proceeds to cover data analysis, probability and all topics crucial to the study of statistics.

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Book SynopsisUnderstanding the world of R programming and analysis has never been easier Most guides to R, whether books or online, focus on R functions and procedures.Table of ContentsIntroduction 1 About This Book 1 Similarity with This Other For Dummies Book 2 What You Can Safely Skip 2 Foolish Assumptions 2 How This Book Is Organized 3 Part 1: Getting Started with Statistical Analysis with R 3 Part 2: Describing Data 3 Part 3: Drawing Conclusions from Data 3 Part 4: Working with Probability 3 Part 5: The Part of Tens 4 Online Appendix A: More on Probability 4 Online Appendix B: Non-Parametric Statistics 4 Online Appendix C: Ten Topics That Just Didn’t Fit in Any Other Chapter 4 Icons Used in This Book 4 Where to Go from Here 5 Part 1: Getting Started with Statistical Analysis with R 7 Chapter 1: Data, Statistics, and Decisions 9 The Statistical (and Related) Notions You Just Have to Know 10 Samples and populations 10 Variables: Dependent and independent 11 Types of data 12 A little probability 13 Inferential Statistics: Testing Hypotheses 14 Null and alternative hypotheses 14 Two types of error 15 Chapter 2: R: What It Does and How It Does It 17 Downloading R and RStudio 18 A Session with R 21 The working directory 21 So let’s get started, already 22 Missing data 26 R Functions 26 User-Defined Functions 28 Comments 29 R Structures 29 Vectors 30 Numerical vectors 30 Matrices 31 Factors 33 Lists 34 Lists and statistics 35 Data frames 36 Packages 39 More Packages 42 R Formulas 43 Reading and Writing 44 Spreadsheets 44 CSV files 46 Text files 47 Part 2: Describing Data 49 Chapter 3: Getting Graphic 51 Finding Patterns 51 Graphing a distribution 52 Bar-hopping 53 Slicing the pie 54 The plot of scatter 55 Of boxes and whiskers 56 Base R Graphics 57 Histograms 57 Adding graph features 59 Bar plots 60 Pie graphs 62 Dot charts 62 Bar plots revisited 64 Scatter plots 67 Box plots 71 Graduating to ggplot2 71 Histograms 72 Bar plots 74 Dot charts 75 Bar plots re-revisited 78 Scatter plots 82 Box plots 86 Wrapping Up 89 Chapter 4: Finding Your Center 91 Means: The Lure of Averages 91 The Average in R: mean() 93 What’s your condition? 93 Eliminate $-signs forth with() 94 Exploring the data 95 Outliers: The flaw of averages 96 Other means to an end 97 Medians: Caught in the Middle 99 The Median in R: median() 100 Statistics à la Mode 101 The Mode in R 101 Chapter 5: Deviating from the Average 103 Measuring Variation 104 Averaging squared deviations: Variance and how to calculate it 104 Sample variance 107 Variance in R 107 Back to the Roots: Standard Deviation 108 Population standard deviation 108 Sample standard deviation 109 Standard Deviation in R 109 Conditions, Conditions, Conditions 110 Chapter 6: Meeting Standards and Standings 111 Catching Some Z’s 112 Characteristics of z-scores 112 Bonds versus the Bambino 113 Exam scores 114 Standard Scores in R 114 Where Do You Stand? 117 Ranking in R 117 Tied scores 117 Nth smallest, Nth largest 118 Percentiles 118 Percent ranks 120 Summarizing 121 Chapter 7: Summarizing It All 123 How Many? 123 The High and the Low 125 Living in the Moments 125 A teachable moment 126 Back to descriptives 126 Skewness 127 Kurtosis 130 Tuning in the Frequency 131 Nominal variables: table() et al 131 Numerical variables: hist() 132 Numerical variables: stem() 138 Summarizing a Data Frame 139 Chapter 8: What’s Normal? 143 Hitting the Curve 143 Digging deeper 144 Parameters of a normal distribution 145 Working with Normal Distributions 147 Distributions in R 147 Normal density function 147 Cumulative density function 152 Quantiles of normal distributions 155 Random sampling 156 A Distinguished Member of the Family 158 Part 3: Drawing Conclusions From Data 161 Chapter 9: The Confidence Game: Estimation 163 Understanding Sampling Distributions 164 An EXTREMELY Important Idea: The Central Limit Theorem 165 (Approximately) Simulating the central limit theorem 167 Predictions of the central limit theorem 171 Confidence: It Has Its Limits! 173 Finding confidence limits for a mean 173 Fit to a t 175 Chapter 10: One-Sample Hypothesis Testing 179 Hypotheses, Tests, and Errors 179 Hypothesis Tests and Sampling Distributions 181 Catching Some Z’s Again 183 Z Testing in R 185 t for One 187 t Testing in R 188 Working with t-Distributions 189 Visualizing t-Distributions 190 Plotting t in base R graphics 191 Plotting t in ggplot2 192 One more thing about ggplot2 197 Testing a Variance 198 Testing in R 199 Working with Chi-Square Distributions 201 Visualizing Chi-Square Distributions 201 Plotting chi-square in base R graphics 202 Plotting chi-square in ggplot2 203 Chapter 11: Two-Sample Hypothesis Testing 205 Hypotheses Built for Two 205 Sampling Distributions Revisited 206 Applying the central limit theorem 207 Z’s once more 208 Z-testing for two samples in R 210 t for Two 212 Like Peas in a Pod: Equal Variances 212 t-Testing in R 214 Working with two vectors 214 Working with a data frame and a formula 215 Visualizing the results 216 Like p’s and q’s: Unequal variances 219 A Matched Set: Hypothesis Testing for Paired Samples 220 Paired Sample t-testing in R 222 Testing Two Variances 222 F-testing in R 224 F in conjunction with t 225 Working with F-Distributions 226 Visualizing F-Distributions 226 Chapter 12: Testing More than Two Samples 231 Testing More Than Two 231 A thorny problem 232 A solution 233 Meaningful relationships 237 ANOVA in R 237 Visualizing the results 239 After the ANOVA 239 Contrasts in R 242 Unplanned comparisons 243 Another Kind of Hypothesis, Another Kind of Test 244 Working with repeated measures ANOVA 245 Repeated measures ANOVA in R 247 Visualizing the results 249 Getting Trendy 250 Trend Analysis in R 254 Chapter 13: More Complicated Testing 255 Cracking the Combinations 255 Interactions 257 The analysis 257 Two-Way ANOVA in R 259 Visualizing the two-way results 261 Two Kinds of Variables at Once 263 Mixed ANOVA in R 266 Visualizing the Mixed ANOVA results 268 After the Analysis 269 Multivariate Analysis of Variance 270 MANOVA in R 271 Visualizing the MANOVA results 273 After the analysis 275 Chapter 14: Regression: Linear, Multiple, and the General Linear Model 277 The Plot of Scatter 277 Graphing Lines 279 Regression: What a Line! 281 Using regression for forecasting 283 Variation around the regression line 283 Testing hypotheses about regression 285 Linear Regression in R 290 Features of the linear model 292 Making predictions 292 Visualizing the scatter plot and regression line 293 Plotting the residuals 294 Juggling Many Relationships at Once: Multiple Regression 295 Multiple regression in R 297 Making predictions 298 Visualizing the 3D scatter plot and regression plane 298 ANOVA: Another Look 301 Analysis of Covariance: The Final Component of the GLM 305 But wait — there’s more 311 Chapter 15: Correlation: The Rise and Fall of Relationships 313 Scatter plots Again 313 Understanding Correlation 314 Correlation and Regression 316 Testing Hypotheses About Correlation 319 Is a correlation coefficient greater than zero? 319 Do two correlation coefficients differ? 320 Correlation in R 322 Calculating a correlation coefficient 322 Testing a correlation coefficient 322 Testing the difference between two correlation coefficients 323 Calculating a correlation matrix 324 Visualizing correlation matrices 324 Multiple Correlation 326 Multiple correlation in R 327 Adjusting R-squared 328 Partial Correlation 329 Partial Correlation in R 330 Semipartial Correlation 331 Semipartial Correlation in R 332 Chapter 16: Curvilinear Regression: When Relationships Get Complicated 335 What Is a Logarithm? 336 What Is e? 338 Power Regression 341 Exponential Regression 346 Logarithmic Regression 350 Polynomial Regression: A Higher Power 354 Which Model Should You Use? 358 Part 4: Working with Probability 359 Chapter 17: Introducing Probability 361 What Is Probability? 361 Experiments, trials, events, and sample spaces 362 Sample spaces and probability 362 Compound Events 363 Union and intersection 363 Intersection again 364 Conditional Probability 365 Working with the probabilities 366 The foundation of hypothesis testing 366 Large Sample Spaces 366 Permutations 367 Combinations 368 R Functions for Counting Rules 369 Random Variables: Discrete and Continuous 371 Probability Distributions and Density Functions 371 The Binomial Distribution 374 The Binomial and Negative Binomial in R 375 Binomial distribution 375 Negative binomial distribution 377 Hypothesis Testing with the Binomial Distribution 378 More on Hypothesis Testing: R versus Tradition 380 Chapter 18: Introducing Modeling 383 Modeling a Distribution 383 Plunging into the Poisson distribution 384 Modeling with the Poisson distribution 385 Testing the model’s fit 388 A word about chisqtest() 391 Playing ball with a model 392 A Simulating Discussion 396 Taking a chance: The Monte Carlo method 396 Loading the dice 396 Simulating the central limit theorem 401 Part 5: The Part of Tens 405 Chapter 19: Ten Tips for Excel Emigrés 407 Defining a Vector in R Is Like Naming a Range in Excel 407 Operating on Vectors Is Like Operating on Named Ranges 408 Sometimes Statistical Functions Work the Same Way 412 And Sometimes They Don’t 412 Contrast: Excel and R Work with Different Data Formats 413 Distribution Functions Are (Somewhat) Similar 414 A Data Frame Is (Something) Like a Multicolumn Named Range 416 The sapply() Function Is Like Dragging 417 Using edit() Is (Almost) Like Editing a Spreadsheet 418 Use the Clipboard to Import a Table from Excel into R 419 Chapter 20: Ten Valuable Online R Resources 421 Websites for R Users 421 R-bloggers 421 Microsoft R Application Network 422 Quick-R 422 RStudio Online Learning 422 Stack Overflow 422 Online Books and Documentation 423 R manuals 423 R documentation 423 RDocumentation 423 YOU CANanalytics 423 The R Journal 424 Index 425

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a huge range and FREE tracked UK delivery on ALL orders.

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a huge range and FREE tracked UK delivery on ALL orders.

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Book SynopsisRandom matrix theory, both as an application and as a theory, has evolved rapidly over the years. This title chronicles these developments, emphasizing log-gases as a physical picture. It covers topics such as beta ensembles and Jack polynomials. It develops the application and theory of Gaussian and circular ensembles of random matrix theory.Trade Review"Log-Gases and Random Matrices is an excellent book. It is bound to become an instant classic and the standard reference to a large body of contemporary random matrix theory. It is a well-written tour through a vast landscape. The contemporary literature is extensively referenced and incorporated in the text, and the material is presented from several perspectives. Forrester has achieved the pedagogical equivalent of Dyson's 'Threefold Way' by writing an advanced monograph appealing equally to physicists, mathematicians, and statisticians."--Steven Joel Miller and Eduardo Duenez, Mathematical ReviewsTable of Contents*FrontMatter, pg. i*Preface, pg. v*Contents, pg. xi*Chapter One. Gaussian Matrix Ensembles, pg. 1*Chapter Two. Circular Ensembles, pg. 53*Chapter Three. Laguerre And Jacobi Ensembles, pg. 85*Chapter Four. The Selberg Integral, pg. 133*Chapter Five. Correlation functions at ss = 2, pg. 186*Chapter Six. Correlation Functions At ss= 1 And 4, pg. 236*Chapter Seven. Scaled limits at ss = 1, 2 and 4, pg. 283*Chapter Eight. Eigenvalue probabilities - Painleve systems approach, pg. 328*Chapter Nine. Eigenvalue probabilities- Fredholm determinant approach, pg. 380*Chapter Ten. Lattice paths and growth models, pg. 440*Chapter Eleven. The Calogero-Sutherland model, pg. 505*Chapter Twelve. Jack polynomials, pg. 543*Chapter Thirteen. Correlations for general ss, pg. 592*Chapter Fourteen. Fluctuation formulas and universal behavior of correlations, pg. 658*Chapter Fifteen. The two-dimensional one-component plasma, pg. 701*Bibliography, pg. 765*Index, pg. 785

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Book SynopsisThis book is a guide to the practical application of statistics in data analysis as typically encountered in the physical sciences. It is primarily addressed at students and professionals who need to draw quantitative conclusions from experimental data. Although most of the examples are taken from particle physics, the material is presented in a sufficiently general way as to be useful to people from most branches of the physical sciences. The first part of the book describes the basic tools of data analysis: concepts of probability and random variables, Monte Carlo techniques, statistical tests, and methods of parameter estimation. The last three chapters are somewhat more specialized than those preceding, covering interval estimation, characteristic functions, and the problem of correcting distributions for the effects of measurement errors (unfolding).Trade Review"Glen Cowan is a particle physicist who seems to have got everything right. Results are stated clearly, without mathematical proof but with enough explanation to satisfy the physicist's need to understand not only how, but also why...Those teaching an advanced undergraduate or graduate course in statistics or physicists will find this a good textbook...Do not be fooled by the fact that it does not have the "textbook look" - the exercises have been made available separately on a Web site. " CERN Courier"The material presented in this book is dense.In less than two hundred pages, it takes the reader from the basic notions of probability, through neural networks, Monte Carlo methods, and regularization techniques." Short Book ReviewsTable of ContentsPreface ; Notation ; 1. Fundamental Concepts ; 2. Examples of Probability Functions ; 3. The Monte Carlo Method ; 4. Statistical Tests ; 5. General Concepts of Parameter Estimation ; 6. The Method of Maximum Likelihood ; 7. The Method of Least Squares ; 8. The Method of Moments ; 9. Statistical Errors, Confidence Intervals and Limits ; 10. Characteristic Functions and Related Examples ; 11. Unfolding ; Bibliography ; Index

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Book SynopsisPraise for George E.P. Box and An Accidental Statistician I found most interesting the parts describing how he developed as a statistician, the intellectual influences on him, and the genesis of the ideas for which he is so well known...Trade ReviewMentioned in The Economist - 20 December 2014Table of ContentsForeword xi Second Foreword xv Preface xix Acknowledgments xxi From ThePublisher xxiii 1 Early Years 1 ‘‘Who in the world am I? Ah, that’s the great puzzle.’’ 2 Army Life 19 ‘‘Contrarywise, if it was so, it might be: and if it were so, it would be: but as it isn’t, it ain’t. That’s logic.’’ 3 ICI and the Statistical Methods Panel 44 ‘‘Can you answer useful questions?’’ 4 George Barnard 53 ‘‘When I use a word . . . it means just what I choose it to mean–neither more nor less.’’ 5 An Invitation to the United States 63 ‘‘The time has come, ‘the walrus said,’ to talk of many things. Of shoes and ships and sealing wax, of cabbages and kings.’’ 6 Princeton 78 ‘‘Ah! Then yours wasn’t a really good school.’’ 7 A New Life in Madison 94 ‘‘Digging for apples, your honor!’’ 8 Time Series 124 ‘‘What do you know about this business?’’ 9 George Tiao and the Bayes Book 139 ‘‘It gets easier further on.’’ 10 GrowingUp (Helen and Harry) 144 ‘‘There are 364 days when you might get unbirthday presents, and only 1 for birthday presents, you know.’’ 11 Fisher—Father and Son 151 ‘‘I only hope the boat won’t tipple over!’’ 12 Bill Hunter and Some Ideas on Experimental Design 157 ‘‘There goes Bill!’’ 13 The Quality Movement 181 ‘‘The race is over!. . . ‘Everybody has won and all must have prizes.’’’ 14 Adventures with Claire 197 ‘‘What else had you to learn?’’ ‘‘Well, there was Mystery.’’ 15 The Many Sides of Mac 209 ‘‘There’s nothing like eating hay when you’re feeling faint.’’ 16 Life in England 218 ‘‘What matters is how far we go? There is another shore, you know, upon the other side.’’ 17 Journeys to Scandinavia 224 ‘‘What sort of people live here?’’ 18 A Second Home in Spain 228 ‘‘I know something interesting is sure to happen.’’ 19 The Royal Society of London 245 20 Conclusion 247 21 Memories 248 Index 265

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Book SynopsisMeta-analysis is a powerful statistical methodology for synthesizing research evidence across independent studies. This is the first comprehensive handbook of meta-analysis written specifically for ecologists and evolutionary biologists, and it provides an invaluable introduction for beginners as well as an up-to-date guide for experienced meta-anaTrade Review"[T]his is a comprehensive and up-to-date compendium of all relevant aspects for meta-analysis conduction in ecology, evolution, and related topics. Scientists from these areas who already have some knowledge on meta-analysis will find valuable guidance."--Daniela Vetter, Quarterly Review of BiologyTable of ContentsPreface xi SECTION I: Introduction & Planning 1.Place of Meta-analysis among Other Methods of Research Synthesis 3 Julia Koricheva & Jessica Gurevitch 2.The Procedure of Meta-analysis in a Nutshell 14 Isabelle M. Cote & Michael D. Jennions SECTION II : Initiating a Meta-analysis 3.First Steps in Beginning a Meta-analysis 27 Gavin B. Stewart, Isabelle M. Cote, Hannah R. Rothstein, & Peter S. Curtis 4.Gathering Data: Searching Literature & Selection Criteria 37 Isabelle M. Cote, Peter S. Curtis, Hannah R. Rothstein, & Gavin B. Stewart 5.Extraction & Critical Appraisal of Data 52 Peter S. Curtis, Kerrie Mengersen, Marc J. Lajeunesse, Hannah R. Rothstein, & Gavin B. Stewart 6.Effect Sizes: Conventional Choices & Calculations 61 Michael S. Rosenberg, Hannah R. Rothstein, & Jessica Gurevitch 7.Using Other Metrics of Effect Size in Meta-analysis 72 Kerrie Mengersen & Jessica Gurevitch SECTION III : Essential Analytic Models & Methods 8.Statistical Models & Approaches to Inference 89 Kerrie Mengersen, Christopher H. Schmid, Michael D. Jennions, & Jessica Gurevitch 9.Moment & Least-Squares Based Approaches to Meta-analytic Inference 108 Michael S. Rosenberg 10.Maximum Likelihood Approaches to Meta-analysis 125 Kerrie Mengersen & Christopher H. Schmid 11.Bayesian Meta-analysis 145 Christopher H. Schmid & Kerrie Mengersen 12.Software for Statistical Meta-analysis 174 Christopher H. Schmid, Gavin B. Stewart, Hannah R. Rothstein, Marc J. Lajeunesse, & Jessica Gurevitch SECTION IV: Statistical Issues & Problems 13.Recovering Missing or Partial Data from Studies: A Survey of Conversions & Imputations for Meta-analysis 195 Marc J. Lajeunesse 14.Publication & Related Biases 207 Michael D. Jennions, Christopher J. Lortie, Michael S. Rosenberg, & Hannah R. Rothstein 15.Temporal Trends in Effect Sizes: Causes, Detection, & Implications 237 Julia Koricheva, Michael D. Jennions, & Joseph Lau 16.Statistical Models for the Meta-analysis of Nonindependent Data 255 Kerrie Mengersen, Michael D. Jennions, & Christopher H. Schmid 17.Phylogenetic Nonindependence & Meta-analysis 284 Marc J. Lajeunesse, Michael S. Rosenberg, & Michael D. Jennions 18.Meta-analysis of Primary Data 300 Kerrie Mengersen, Jessica Gurevitch, & Christopher H. Schmid 19.Meta-analysis of Results from Multisite Studies 313 Jessica Gurevitch SECTION V: Presentation & Interpretation of Results 20.Quality St&ards for Research Syntheses 323 Hannah R. Rothstein, Christopher J. Lortie, Gavin B. Stewart, Julia Koricheva, & Jessica Gurevitch 21.Graphical Presentation of Results 339 Christopher J. Lortie, Joseph Lau, & Marc J. Lajeunesse 22.Power Statistics for Meta-analysis: Tests for Mean Effects & Homogeneity 348 Marc J. Lajeunesse 23.Role of Meta-analysis in Interpreting the Scientific Literature 364 Michael D. Jennions, Christopher J. Lortie, & Julia Koricheva 24.Using Meta-analysis to Test Ecological & Evolutionary Theory 381 Michael D. Jennions, Christopher J. Lortie, & Julia Koricheva SECTION VI: Contributions of Meta-analysis in Ecology & Evolution 25.History & Progress of Meta-analysis 407 Joseph Lau, Hannah R. Rothstein, & Gavin B. Stewart 26.Contributions of Meta-analysis to Conservation & Management 420 Isabelle M. Cote & Gavin B. Stewart 27.Conclusions: Past, Present, & Future of Meta-analysis in Ecology & Evolution 426 Jessica Gurevitch & Julia Koricheva Glossary 433 Frequently Asked Questions 441 References 447 List of Contributors 487 Subject Index 489

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Book SynopsisGeneralized Estimating Equations, Second Edition updates the best-selling previous edition, which has been the standard text on the subject since it was published a decade ago. Combining theory and application, the text provides readers with a comprehensive discussion of GEE and related models. Numerous examples are employed throughout the text, along with the software code used to create, run, and evaluate the models being examined. Stata is used as the primary software for running and displaying modeling output; associated R code is also given to allow R users to replicate Stata examples. Specific examples of SAS usage are provided in the final chapter as well as on the book's website.This second edition incorporates comments and suggestions from a variety of sources, including the Statistics.com course on longitudinal and panel models taught by the authors. Other enhancements include an examination of GEE marginal effects; a more thorough presentatiTrade Review"Overall, I found this to be a very useful book on GEE, and would recommend it to anyone planning to use GEE models in their data analysis. Both the theory and practical aspects of constructing and analysing such models is covered. Inclusion of code for many of the analyses is an excellent feature."—Ken J. Beath, Macquarie University, Australia, Australian and New Zealand Journal of Statistics, April 2017" … the authors expand the text with several additions: (I) they examine and include entirely new topics related to GEE and the estimation of clustered and longitudinal models; (2) they add more detailed discussions of previously presented topics, including expanding the discussion of various models associated with GEE (penalized GEE, survey GEE, and quasi-least-square regression), adding material on hypothesis testing and diagnostics, and introducing alternative models for ordered categorical outcomes and an extension of the QIC, which is a model selection criterion measure; (3) they expand the amount of computer code by adding R code to duplicate the Stata examples wherever possible. In my opinion, the second edition is enhanced by the additions mentioned above, providing an excellent review of the GEE, wide coverage of its variations, and many useful computing techniques. I believe it would be a very useful reference book for practicing researchers and graduate students who are interested in research topics related to GEE."—CindyYu, Iowa State University in the Journal of the American Statistical Association, December 2013"The second edition … adds a few new topics related to various extensions of GEE … [and replaces] outdated S-PLUS codes with R scripts. Also, the number of exercises increased significantly … . For those who want to use this book in the classroom, including me, having extra exercise sets is certainly a welcome addition. … One main strength of this book is its comprehensive coverage of Stata implementation of the GEE. … a valuable reference and is particularly useful for practitioners. It can serve as supplemental reading in longitudinal data analysis classes as well."—Woncheol Jang, Biometrics, September 2013Praise for the First Edition:"… well-written chapters … . The book contains challenging problems in exercises and is suitable to be a textbook in a graduate-level course on estimating functions. The references are up-to-date and exhaustive. … I enjoyed reading [this book] and recommend [it] very highly to the statistical community."—Journal of Statistical Computation and Simulation, February 2005"[The book] is comprehensive and covers much useful material with formulas presented in detail … a useful and recommendable book both for those who already work with GEE methods and for newcomers to the field."—Per Kragh Andersen, University of Copenhagen, Statistics in Medicine, 2004"Generalized Estimating Equations is the first and only book to date dedicated exclusively to generalized estimating equations (GEE). I find it to be a good reference text for anyone using generalized linear models (GLIM).The authors do a good job of not only presenting the general theory of GEE models, but also giving explicit examples of various correlation structures, link functions and a comparison between population-averaged and subject-specific models. Furthermore, there are sections on the analysis of residuals, deletion diagnostics, goodness-of-fit criteria, and hypothesis testing. Good data-driven examples that give comparisons between different GEE models are provided throughout the book. Perhaps the greatest strength of this book is its completeness. It is a thorough compendium of information from the GEE literature. Overall, Generalized Estimating Equations contains a unique survey of GEE models in an attempt to unify notation and provide the most in-depth treatment of GEEs. I believe that it serves as a valuable reference for researchers, teachers, and students who study and practice GLIM methodology."—Journal of the American Statistics Association, March 2004"Generalized Estimating Equations is a good introductory book for analysing continuous and discrete data using GEE methods ... . This book is easy to read, and it assumes that the reader has some background in GLM. Many examples are drawn from biomedical studies and survey studies, and so it provides good guidance for analysing correlated data in these and other areas."—Technometrics, 2003"Overall, I found this to be a very useful book on GEE, and would recommend it to anyone planning to use GEE models in their data analysis. Both the theory and practical aspects of constructing and analysing such models is covered. Inclusion of code for many of the analyses is an excellent feature."—Ken J. Beath, Macquarie University, Australia, Australian and New Zealand Journal of Statistics, April 2017"The second edition … adds a few new topics related to various extensions of GEE … [and replaces] outdated S-PLUS codes with R scripts. Also, the number of exercises increased significantly … . For those who want to use this book in the classroom, including me, having extra exercise sets is certainly a welcome addition. … One main strength of this book is its comprehensive coverage of Stata implementation of the GEE. … a valuable reference and is particularly useful for practitioners. It can serve as supplemental reading in longitudinal data analysis classes as well."—Woncheol Jang, Biometrics, September 2013Praise for the First Edition:"… well-written chapters … . The book contains challenging problems in exercises and is suitable to be a textbook in a graduate-level course on estimating functions. The references are up-to-date and exhaustive. … I enjoyed reading [this book] and recommend [it] very highly to the statistical community."—Journal of Statistical Computation and Simulation, February 2005"[The book] is comprehensive and covers much useful material with formulas presented in detail … a useful and recommendable book both for those who already work with GEE methods and for newcomers to the field."—Per Kragh Andersen, University of Copenhagen, Statistics in Medicine, 2004"Generalized Estimating Equations is the first and only book to date dedicated exclusively to generalized estimating equations (GEE). I find it to be a good reference text for anyone using generalized linear models (GLIM).The authors do a good job of not only presenting the general theory of GEE models, but also giving explicit examples of various correlation structures, link functions and a comparison between population-averaged and subject-specific models. Furthermore, there are sections on the analysis of residuals, deletion diagnostics, goodness-of-fit criteria, and hypothesis testing. Good data-driven examples that give comparisons between different GEE models are provided throughout the book. Perhaps the greatest strength of this book is its completeness. It is a thorough compendium of information from the GEE literature. Overall, Generalized Estimating Equations contains a unique survey of GEE models in an attempt to unify notation and provide the most in-depth treatment of GEEs. I believe that it serves as a valuable reference for researchers, teachers, and students who study and practice GLIM methodology."—Journal of the American Statistics Association, March 2004"Generalized Estimating Equations is a good introductory book for analysing continuous and discrete data using GEE methods ... . This book is easy to read, and it assumes that the reader has some background in GLM. Many examples are drawn from biomedical studies and survey studies, and so it provides good guidance for analysing correlated data in these and other areas."—Technometrics, 2003Table of ContentsIntroduction. Model Construction and Estimating Equations. Generalized Estimating Equations. Residuals, Diagnostics, and Testing. Programs and Datasets. References. Author Index. Subject Index.

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Book SynopsisAn important factor that affects the duration, complexity and cost of a clinical trial is the endpoint used to study the treatmentâs efficacy. When a true endpoint is difficult to use because of such factors as long follow-up times or prohibitive cost, it is sometimes possible to use a surrogate endpoint that can be measured in a more convenient or cost-effective way. This book focuses on the use of surrogate endpoint evaluation methods in practice, using SAS and R.Trade Review"This is a timely text. The number of published studies using surrogate endpoints has increased dramatically since the early work of the 1980s; however, there is a dearth of available texts or software on this topic. Anyone with an interest in surrogate endpoint evaluation would benefit from this text."~Statistics in Medicine Table of ContentsIntroductory Material. Introduction. Notation and Example Datasets. The History of Surrogate Endpoint Validation. Contemporary Surrogate Endpoint Evaluation Methods. Multiple-Trial Surrogate Endpoint Evaluation Methods. Two Continuous Outcomes. Two Survival Endpoints. Two Categorical Endpoints. A Categorical and a Continuous Endpoint. A Survival and a Continuous Endpoint. A Survival and a Categorical Endpoint. Two Longitudinal Endpoints. A Longitudinal and a Survival Endpoint. Additional Considerations and Further Topics. Software Details. An Alternative Surrogate Endpoint Evaluation Framework: Causal-Inference. Surrogate Endpoint Evaluation Methods in Small Samples. Construction and Evaluation of Genetic Biomarkers in Early Drug Development Experiments. Additional Considerations.

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Book SynopsisNATIONAL BESTSELLER • From the classroom to the courtroom and from financial markets to supermarkets, an intriguing and illuminating look at how randomness, chance, and probability affect our daily lives that will intrigue, awe, and inspire.“Mlodinow writes in a breezy style, interspersing probabilistic mind-benders with portraits of theorists.... The result is a readable crash course in randomness.” —The New York Times Book ReviewWith the born storyteller's command of narrative and imaginative approach, Leonard Mlodinow vividly demonstrates how our lives are profoundly informed by chance and randomness and how everything from wine ratings and corporate success to school grades and political polls are less reliable than we believe.By showing us the true nature of chance and revealing the psychological illusions that cause us to misjudge the world around us, Mlodinow gives us the tools we need to make more

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Book SynopsisPraise for the Second Edition "A must-have book for anyone expecting to do research and/or applications in categorical data analysis. " Statistics in Medicine "It is a total delight reading this book.Table of ContentsPreface xiii 1 Introduction: Distributions and Inference for Categorical Data 1 1.1 Categorical Response Data, 1 1.2 Distributions for Categorical Data, 5 1.3 Statistical Inference for Categorical Data, 8 1.4 Statistical Inference for Binomial Parameters, 13 1.5 Statistical Inference for Multinomial Parameters, 17 1.6 Bayesian Inference for Binomial and Multinomial Parameters, 22 Notes, 27 Exercises, 28 2 Describing Contingency Tables 37 2.1 Probability Structure for Contingency Tables, 37 2.2 Comparing Two Proportions, 43 2.3 Conditional Association in Stratified 2 × 2 Tables, 47 2.4 Measuring Association in I × J Tables, 54 Notes, 60 Exercises, 60 3 Inference for Two-Way Contingency Tables 69 3.1 Confidence Intervals for Association Parameters, 69 3.2 Testing Independence in Two-way Contingency Tables, 75 3.3 Following-up Chi-Squared Tests, 80 3.4 Two-Way Tables with Ordered Classifications, 86 3.5 Small-Sample Inference for Contingency Tables, 90 3.6 Bayesian Inference for Two-way Contingency Tables, 96 3.7 Extensions for Multiway Tables and Nontabulated Responses, 100 Notes, 101 Exercises, 103 4 Introduction to Generalized Linear Models 113 4.1 The Generalized Linear Model, 113 4.2 Generalized Linear Models for Binary Data, 117 4.3 Generalized Linear Models for Counts and Rates, 122 4.4 Moments and Likelihood for Generalized Linear Models, 130 4.5 Inference and Model Checking for Generalized Linear Models, 136 4.6 Fitting Generalized Linear Models, 143 4.7 Quasi-Likelihood and Generalized Linear Models, 149 Notes, 152 Exercises, 153 5 Logistic Regression 163 5.1 Interpreting Parameters in Logistic Regression, 163 5.2 Inference for Logistic Regression, 169 5.3 Logistic Models with Categorical Predictors, 175 5.4 Multiple Logistic Regression, 182 5.5 Fitting Logistic Regression Models, 192 Notes, 195 Exercises, 196 6 Building, Checking, and Applying Logistic Regression Models 207 6.1 Strategies in Model Selection, 207 6.2 Logistic Regression Diagnostics, 215 6.3 Summarizing the Predictive Power of a Model, 221 6.4 Mantel–Haenszel and Related Methods for Multiple 2 × 2 Tables, 225 6.5 Detecting and Dealing with Infinite Estimates, 233 6.6 Sample Size and Power Considerations, 237 Notes, 241 Exercises, 243 7 Alternative Modeling of Binary Response Data 251 7.1 Probit and Complementary Log–log Models, 251 7.2 Bayesian Inference for Binary Regression, 257 7.3 Conditional Logistic Regression, 265 7.4 Smoothing: Kernels, Penalized Likelihood, Generalized Additive Models, 270 7.5 Issues in Analyzing High-Dimensional Categorical Data, 278 Notes, 285 Exercises, 287 8 Models for Multinomial Responses 293 8.1 Nominal Responses: Baseline-Category Logit Models, 293 8.2 Ordinal Responses: Cumulative Logit Models, 301 8.3 Ordinal Responses: Alternative Models, 308 8.4 Testing Conditional Independence in I × J × K Tables, 314 8.5 Discrete-Choice Models, 320 8.6 Bayesian Modeling of Multinomial Responses, 323 Notes, 326 Exercises, 329 9 Loglinear Models for Contingency Tables 339 9.1 Loglinear Models for Two-way Tables, 339 9.2 Loglinear Models for Independence and Interaction in Three-way Tables, 342 9.3 Inference for Loglinear Models, 348 9.4 Loglinear Models for Higher Dimensions, 350 9.5 Loglinear—Logistic Model Connection, 353 9.6 Loglinear Model Fitting: Likelihood Equations and Asymptotic Distributions, 356 9.7 Loglinear Model Fitting: Iterative Methods and Their Application, 364 Notes, 368 Exercises, 369 10 Building and Extending Loglinear Models 377 10.1 Conditional Independence Graphs and Collapsibility, 377 10.2 Model Selection and Comparison, 380 10.3 Residuals for Detecting Cell-Specific Lack of Fit, 385 10.4 Modeling Ordinal Associations, 386 10.5 Generalized Loglinear and Association Models, Correlation Models, and Correspondence Analysis, 393 10.6 Empty Cells and Sparseness in Modeling Contingency Tables, 398 10.7 Bayesian Loglinear Modeling, 401 Notes, 404 Exercises, 407 11 Models for Matched Pairs 413 11.1 Comparing Dependent Proportions, 414 11.2 Conditional Logistic Regression for Binary Matched Pairs, 418 11.3 Marginal Models for Square Contingency Tables, 424 11.4 Symmetry, Quasi-Symmetry, and Quasi-Independence, 426 11.5 Measuring Agreement Between Observers, 432 11.6 Bradley–Terry Model for Paired Preferences, 436 11.7 Marginal Models and Quasi-Symmetry Models for Matched Sets, 439 Notes, 443 Exercises, 445 12 Clustered Categorical Data: Marginal and Transitional Models 455 12.1 Marginal Modeling: Maximum Likelihood Approach, 456 12.2 Marginal Modeling: Generalized Estimating Equations (GEEs) Approach, 462 12.3 Quasi-Likelihood and Its GEE Multivariate Extension: Details, 465 12.4 Transitional Models: Markov Chain and Time Series Models, 473 Notes, 478 Exercises, 479 13 Clustered Categorical Data: Random Effects Models 489 13.1 Random Effects Modeling of Clustered Categorical Data, 489 13.2 Binary Responses: Logistic-Normal Model, 494 13.3 Examples of Random Effects Models for Binary Data, 498 13.4 Random Effects Models for Multinomial Data, 511 13.5 Multilevel Modeling, 515 13.6 GLMM Fitting, Inference, and Prediction, 519 13.7 Bayesian Multivariate Categorical Modeling, 523 Notes, 525 Exercises, 527 14 Other Mixture Models for Discrete Data 535 14.1 Latent Class Models, 535 14.2 Nonparametric Random Effects Models, 542 14.3 Beta-Binomial Models, 548 14.4 Negative Binomial Regression, 552 14.5 Poisson Regression with Random Effects, 555 Notes, 557 Exercises, 558 15 Non-Model-Based Classification and Clustering 565 15.1 Classification: Linear Discriminant Analysis, 565 15.2 Classification: Tree-Structured Prediction, 570 15.3 Cluster Analysis for Categorical Data, 576 Notes, 581 Exercises, 582 16 Large- and Small-Sample Theory for Multinomial Models 587 16.1 Delta Method, 587 16.2 Asymptotic Distributions of Estimators of Model Parameters and Cell Probabilities, 592 16.3 Asymptotic Distributions of Residuals and Goodness-of-fit Statistics, 594 16.4 Asymptotic Distributions for Logit/Loglinear Models, 599 16.5 Small-Sample Significance Tests for Contingency Tables, 601 16.6 Small-Sample Confidence Intervals for Categorical Data, 603 16.7 Alternative Estimation Theory for Parametric Models, 610 Notes, 615 Exercises, 616 17 Historical Tour of Categorical Data Analysis 623 17.1 Pearson–Yule Association Controversy, 623 17.2 R. A. Fisher’s Contributions, 625 17.3 Logistic Regression, 627 17.4 Multiway Contingency Tables and Loglinear Models, 629 17.5 Bayesian Methods for Categorical Data, 633 17.6 A Look Forward, and Backward, 634 Appendix A Statistical Software for Categorical Data Analysis 637 Appendix B Chi-Squared Distribution Values 641 References 643 Author Index 689 Example Index 701 Subject Index 705 Appendix C Software Details for Text Examples (text website)

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Book SynopsisEmphasizes the strategy of experimentation, data analysis, and the interpretation of experimental results. * Features numerous examples using actual engineering and scientific studies. * Presents statistics as an integral component of experimentation from the planning stage to the presentation of the conclusions.Trade Review"With an excellent presentation, this is suitable as a textbook in a graduate level course in design of experiments." (Journal of Statistical Computation and Simulation, April 2005) "...can really provide useful information for the intended audience..." (Zentralblatt Math, Vol. 1029, 2004) “...a practitioner’s guide to statistical methods for designing and analyzing experiments...” (Quarterly of Applied Mathematics, Vol. LXI, No. 3, September 2003) "...a perfect desktop reference..." (Technometrics, Vol. 45, No. 3, August 2003)Table of ContentsPreface. PART I: FUNDAMENTAL STATISTICAL CONCEPTS. Statistics in Engineering and Science. Fundamentals of Statistical Inference. Inferences on Means and Standard Deviations. PART II: DESIGN AND ANALYSIS WITH FACTORIAL STRUCTURE. Statistical Principles in Experimental Design. Factorial Experiments in Completely Randomized Designs. Analysis of Completely Randomized Designs. Fractional Factorial Experiments. Analysis of Fractional Factorial Experiments. PART III: DESIGN AND ANALYSIS WITH RANDOM EFFECTS. Experiments in Randomized Block Designs. Analysis of Designs with Random Factor Levels. Nested Designs. Special Designs for Process Improvement. Analysis of Nested Designs and Designs for Process Improvement. PART IV: DESIGN AND ANALYSIS WITH QUANTITATIVE PREDICTORS AND FACTORS. Linear Regression with One Predicator Variables. Linear Regression with Several Predicator Variables. Linear Regression with Factors and Covariates as Predictors. Designs and Analyses for Fitting Re sponse Surfaces. Model Assessment. Variable Selection Techniques. Appendix: Statistical Tables. Index.

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Book SynopsisStatistics in unusual in its emphasis on the models that underlie statistical inference. The authors make the models comprehensible and show why choosing the wrong model can lead students astray. Carefully constructed exercises in every chapter offer practice in computational skills. Other call for rough estimates and qualitative judgments, so students are forced to come to grips with the concepts instead of mechanically applied formulas. Most sections close with an exercise set; the answers are in the back of the book, often with complete solutions. Chapters also have review exercises, without answers, for homework and tests. Illustrations are in integral part of the exposition. Beginners learn how to read histograms and scatterplots and how to think about these graphics in the context of real problems.

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Book SynopsisExam board: Cambridge Assessment International EducationLevel: A-levelSubject: MathematicsFirst teaching: September 2018First exams: Summer 2020Endorsed by Cambridge Assessment International Education to provide full support for Paper 6 of the syllabus for examination from 2020.Take mathematical understanding to the next level with this accessible series, written by experienced authors, examiners and teachers.- Improve confidence as a mathematician with clear explanations, worked examples, diverse activities and engaging discussion points. - Advance problem-solving, interpretation and communication skills through a wealth of questions that promote higher-order thinking. - Prepare for further study or life beyond the classroom by applying mathematics to other subjects and modelling real-world situations.- Reinforce learning with opportunities for digital practice via links to the Mathematics in Education and Industry's (MEI) Integral platform in the eBook.**To have full access to the eBook and Integral resources you must be subscribed to both Boost and Integral. To trial our eBooks and/or subscribe to Boost, visit: www.hoddereducation.com/Boost; to view samples of the Integral resources and/or subscribe to Integral, visit integralmaths.org/internationalPlease note that the Integral resources have not been through the Cambridge International endorsement process. This book covers the syllabus content for Probability and Statistics 2, including the Poisson distribution, linear combinations of random variables, continuous random variables, sampling and estimation and hypothesis tests.

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Book SynopsisLimitations of Linear Regression Applied on Ecological Data.- Things are not Always Linear; Additive Modelling.- Dealing with Heterogeneity.- Mixed Effects Modelling for Nested Data.- Violation of Independence Part I.- Violation of Independence Part II.- Meet the Exponential Family.- GLM and GAM for Count Data.- GLM and GAM for AbsencePresence and Proportional Data.- Zero-Truncated and Zero-Inflated Models for Count Data.- Generalised Estimation Equations.- GLMM and GAMM.- Estimating Trends for Antarctic Birds in Relation to Climate Change.- Large-Scale Impacts of Land-Use Change in a Scottish Farming Catchment.- Negative Binomial GAM and GAMM to Analyse Amphibian Roadkills.- Additive Mixed Modelling Applied on Deep-Sea Pelagic Bioluminescent Organisms.- Additive Mixed Modelling Applied on Phytoplankton Time Series Data.- Mixed Effects Modelling Applied on American Foulbrood Affecting Honey Bees Larvae.- Three-Way Nested Data for Age Determination Techniques Applied to Cetaceans.- GLTrade ReviewFrom the reviews:"For many people dealing with statistics is like jumping into ice-cold water. This metaphor is depicted by the cover of this book … . full of excellent example code and for most graphs and analyses the code is printed and explained in detail. … Each example finishes with … valuable information for a person new to a technique. In summary, I highly recommend the book to anyone who is familiar with basic statistics … who wants to expand his/her statistical knowledge to analyse ecological data." (Bernd Gruber, Basic and Applied Ecology, Vol. 10, 2009)"This book is written in a very approachable conversational style. The additional focus on the heuristics of the process rather than just a rote recital of theory and equations is commendable. This type of approach helps the reader get behind the ‘why’ of what’s being done rather than blindly follow a simple list of rules.… In short, this text is good for researchers with at least a little familiarity with the basic concepts of modeling and who want some solid stop-by-stop guidance with examples on how common ecological modeling tasks are accomplished using R." (Aaron Christ, Journal of Statistical Software, November 2009, Vol. 32)"The authors succeed in explaining complex extensions of regression in largely nonmathematical terms and clearly present appropriate R code for each analysis. A major strength of the text is that instead of relying on idealized datasets … the authors use data from consulting projects or dissertation research to expose issues associated with ‘real’ data. … The book is well written and accessible … . the volume should be a useful reference for advanced graduate students, postdoctoral researchers, and experienced professionals working in the biological sciences." (Paul E. Bourdeau, The Quarterly Review of Biology, Vol. 84, December, 2009)“This is a companion volume to Analyzing Ecology Data by the same authors. …It extends the previous work by looking at more complex general and generalized linear models involving mixed effects or heterogeneity in variances. It is aimed at statistically sophisticated readers who have a good understanding of multiple regression models… .The pedagogical style is informal… . The authors are pragmatists—they use combinations of informal graphical approaches, formal hypothesis testing, and information-theoretical model selection methods when analyzing data. …Advanced graduate students in ecology or ecologists with several years of experience with ‘messy’ data would find this book useful. …Statisticians would find this book interesting for the nice explorations of many of the issues with messy data. This book would be (very) suitable for a graduate course on statistical consulting—indeed, students would learn a great deal about the use of sophisticated statistical models in ecology! …I very much liked this book (and also the previous volume). I enjoyed the nontechnical presentations of the complex ideas and their emphasis that a good analysis uses ‘simple statistical methods wherever possible, but doesn’t use them simplistically.’” (Biometrics, Summer 2009, 65, 992–993)“This book is a great introduction to a wide variety of regression models. … This text examines how to fit many alternative models using the statistical package R. … The text is a valuable reference … . A large number of real datasets are used as examples. Discussion on which model to use and the large number of recent references make the book useful for self study … .” (David J. Olive, Technometrics, Vol. 52 (4), November, 2010)Table of ContentsLimitations of linear regression applied on ecological data. - Things are not always linear; additive modelling. - Dealing with hetergeneity. - Mixed modelling for nested data. - Violation of independence - temporal data. - Violation of independence; spatial data. - Generalised linear modelling and generalised additive modelling. - Generalised estimation equations. - GLMM and GAMM. - Estimating trends for Antarctic birds in relation to climate change. - Large-scale impacts of land-use change in a Scottish farming catchment. - Negative binomial GAM and GAMM to analyse amphibian road killings. - Additive mixed modelling applied on deep-sea plagic bioluminescent organisms. - Additive mixed modelling applied on phyoplankton time series data. - Mixed modelling applied on American Fouldbrood affecting honey bees larvae. - Three-way nested data for age determination techniques applied to small cetaceans. - GLMM applied on the spatial distribution of koalas in a fragmented landscape. - GEE and GLMM applied on binomial Badger activity data.

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Book SynopsisFay and Brittain present statistical hypothesis testing and compatible confidence intervals, focusing on application and proper interpretation. The emphasis is on equipping applied statisticians with enough tools - and advice on choosing among them - to find reasonable methods for almost any problem and enough theory to tackle new problems by modifying existing methods. After covering the basic mathematical theory and scientific principles, tests and confidence intervals are developed for specific types of data. Essential methods for applications are covered, such as general procedures for creating tests (e.g., likelihood ratio, bootstrap, permutation, testing from models), adjustments for multiple testing, clustering, stratification, causality, censoring, missing data, group sequential tests, and non-inferiority tests. New methods developed by the authors are included throughout, such as melded confidence intervals for comparing two samples and confidence intervals associated with WilTrade Review'A necessary book for the applied statistician seeking to understand the theoretical underpinnings of statistical methods and for graduate students knowledgeable about statistical theory but lacking experience in application. The book is chock full of challenging examples that point to the complexities of choice of method. A particularly valuable feature of the book is the authors' description of competing methods coupled with their clarity in explaining and justifying why they prefer one method over others. Fay and Brittain should sit on every statistician's bookshelf.' Janet Wittes, WCG Statistics Collaborative'Good statistical hypothesis testing and confidence interval construction involves mathematical aspects of finding a good test given a probability model and scientific aspects of determining the appropriateness of a probability model for answering a scientific question. This book provides a lucid discussion of both these mathematical and scientific aspects with compelling scientific examples. I most highly recommend this book.' Dylan Small, University of Pennsylvania'Congratulations to Fay and Brittain for this wonderful reference book that does what its somewhat unusual title suggests: puts hypothesis testing in the context of science. The vast coverage of topics, extensive bibliography and notes, and easy to understand explanations make 'Statistical Hypothesis Testing in Context: Reproducibility, Inference, and Science' an indispensable tool in the arsenal of any applied or theoretical statistician or biostatistician. I enthusiastically recommend buying the book!' Michael A. Proschan, National Institute of Allergy and Infectious DiseasesTable of Contents1. Introduction; 2. Theory of tests, p-values, and confidence intervals; 3. From scientific theory to statistical hypothesis test; 4. One sample studies with binary responses; 5. One sample studies with ordinal or numeric responses; 6. Paired data; 7. Two sample studies with binary responses; 8. Assumptions and hypothesis tests; 9. Two sample studies with ordinal or numeric responses; 10. General methods for creating decision rules; 11. K-Sample studies and trend tests; 12. Clustering and stratification; 13. Multiplicity in testing; 14. Testing from models; 15. Causality; 16. Censoring; 17. Missing data; 18. Group sequential and related adaptive methods; 19. Testing fit, equivalence, and non-inferiority; 20. Power and sample size.

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