In this lively and groundbreaking new book, economist Ian Ayres shows how today's best and brightest organizations are analyzing massive databases at lightening speed to provide greater insights into human behavior. They are the Super Crunchers. From internet sites like Google and Amazon that know your tastes better than you do, to a physician's diagnosis and your child's education, to boardrooms and government agencies, this new breed of decision makers are calling the shots. And they are delivering staggeringly accurate results. How can a football coach evaluate a player without ever seeing him play? Want to know whether the price of an airline ticket will go up or down before you buy? How can a formula outpredict wine experts in determining the best vintages? Super crunchers have the answers. In this brave new world of equation versus expertise, Ayres shows us the benefits and risks, who loses and who wins, and how super crunching can be used to help, not manipulate us.Gone are the days of solely relying on intuition to make decisions. No businessperson, consumer, or student who wants to stay ahead of the curve should make another keystroke without reading Super Crunchers.

    Machine learning provides these, developing methods that can automatically detect patterns in data and then use the uncovered patterns to predict future data. This textbook offers a comprehensive and self-contained introduction to the field of machine learning, based on a unified, probabilistic approach.The coverage combines breadth and depth, offering necessary background material on such topics as probability, optimization, and linear algebra as well as discussion of recent developments in the field, including conditional random fields, L1 regularization, and deep learning. The book is written in an informal, accessible style, complete with pseudo-code for the most important algorithms. All topics are copiously illustrated with color images and worked examples drawn from such application domains as biology, text processing, computer vision, and robotics. Rather than providing a cookbook of different heuristic methods, the book stresses a principled model-based approach, often using the language of graphical models to specify models in a concise and intuitive way. Almost all the models described have been implemented in a MATLAB software package—PMTK (probabilistic modeling toolkit)—that is freely available online. The book is suitable for upper-level undergraduates with an introductory-level college math background and beginning graduate students.

    Discovered by an 18th century mathematician and preacher, Bayes' rule is a cornerstone of modern probability theory. In this richly illustrated book, intuitive visual representations of real-world examples are used to show how Bayes' rule is actually a form of commonsense reasoning. The tutorial style of writing, combined with a comprehensive glossary, makes this an ideal primer for novices who wish to gain an intuitive understanding of Bayesian analysis. As an aid to understanding, online computer code (in MatLab, Python and R) reproduces key numerical results and diagrams.Stone's book is renowned for its visually engaging style of presentation, which stems from teaching Bayes' rule to psychology students for over 10 years as a university lecturer.

    Its techniques are widely applied in engineering, science, finance, and commerce. This book is designed for a short course on machine learning. It is a short course, not a hurried course. From over a decade of teaching this material, we have distilled what we believe to be the core topics that every student of the subject should know. We chose the title `learning from data' that faithfully describes what the subject is about, and made it a point to cover the topics in a story-like fashion. Our hope is that the reader can learn all the fundamentals of the subject by reading the book cover to cover. ---- Learning from data has distinct theoretical and practical tracks. In this book, we balance the theoretical and the practical, the mathematical and the heuristic. Our criterion for inclusion is relevance. Theory that establishes the conceptual framework for learning is included, and so are heuristics that impact the performance of real learning systems. ---- Learning from data is a very dynamic field. Some of the hot techniques and theories at times become just fads, and others gain traction and become part of the field. What we have emphasized in this book are the necessary fundamentals that give any student of learning from data a solid foundation, and enable him or her to venture out and explore further techniques and theories, or perhaps to contribute their own. ---- The authors are professors at California Institute of Technology (Caltech), Rensselaer Polytechnic Institute (RPI), and National Taiwan University (NTU), where this book is the main text for their popular courses on machine learning. The authors also consult extensively with financial and commercial companies on machine learning applications, and have led winning teams in machine learning competitions.

    This book gives you a solid understanding of statistics without being too simple, yet without the numbing complexity of most college texts. You get a firm grasp of the fundamentals and a hands-on understanding of how to apply them before moving on to the more advanced material that follows. Each chapter presents you with easy-to-follow descriptions illustrated by graphics, formulas, and plenty of solved examples. Before you know it, you'll learn to apply statistical reasoning and statistical techniques, from basic concepts of probability and hypothesis testing to multivariate analysis. Organized into four distinct sections, Statistics in a Nutshell offers you:Introductory material: Different ways to think about statistics Basic concepts of measurement and probability theoryData management for statistical analysis Research design and experimental design How to critique statistics presented by others Basic inferential statistics: Basic concepts of inferential statistics The concept of correlation, when it is and is not an appropriate measure of association Dichotomous and categorical data The distinction between parametric and nonparametric statistics Advanced inferential techniques: The General Linear Model Analysis of Variance (ANOVA) and MANOVA Multiple linear regression Specialized techniques: Business and quality improvement statistics Medical and public health statistics Educational and psychological statistics Unlike many introductory books on the subject, Statistics in a Nutshell doesn't omit important material in an effort to dumb it down. And this book is far more practical than most college texts, which tend to over-emphasize calculation without teaching you when and how to apply different statistical tests. With Statistics in a Nutshell, you learn how to perform most common statistical analyses, and understand statistical techniques presented in research articles. If you need to know how to use a wide range of statistical techniques without getting in over your head, this is the book you want.

    Politicians and marketers present shoddy evidence for dubious claims all the time. But smart people make mistakes too, and when it comes to statistics, plenty of otherwise great scientists--yes, even those published in peer-reviewed journals--are doing statistics wrong."Statistics Done Wrong" comes to the rescue with cautionary tales of all-too-common statistical fallacies. It'll help you see where and why researchers often go wrong and teach you the best practices for avoiding their mistakes.In this book, you'll learn: - Why "statistically significant" doesn't necessarily imply practical significance- Ideas behind hypothesis testing and regression analysis, and common misinterpretations of those ideas- How and how not to ask questions, design experiments, and work with data- Why many studies have too little data to detect what they're looking for-and, surprisingly, why this means published results are often overestimates- Why false positives are much more common than "significant at the 5% level" would suggestBy walking through colorful examples of statistics gone awry, the book offers approachable lessons on proper methodology, and each chapter ends with pro tips for practicing scientists and statisticians. No matter what your level of experience, "Statistics Done Wrong" will teach you how to be a better analyst, data scientist, or researcher.

    Subsequent sections deal with integrating factors; dilution and accretion problems; linearization of first order systems; Laplace Transforms; Newton's Interpolation Formulas, more.

     Offers extensively updated coverage, new problem sets, and chapter-ending material to enhance the book’s relevance to today’s engineers and scientists. Includes new problem sets demonstrating updated applications to engineering as well as biological, physical, and computer science. Emphasizes key ideas as well as the risks and hazards associated with practical application of the material. Includes new material on topics including: difference between discrete and continuous measurements; binary data; quartiles; importance of experimental design; “dummy” variables; rules for expectations and variances of linear functions; Poisson distribution; Weibull and lognormal distributions; central limit theorem, and data plotting. Introduces Bayesian statistics, including its applications to many fields. For those interested in learning more about probability and statistics.

    Polya, How to Solve It will show anyone in any field how to think straight. In lucid and appealing prose, Polya reveals how the mathematical method of demonstrating a proof or finding an unknown can be of help in attacking any problem that can be reasoned out--from building a bridge to winning a game of anagrams. Generations of readers have relished Polya's deft--indeed, brilliant--instructions on stripping away irrelevancies and going straight to the heart of the problem.

    They are established tools in a wide range of industrial applications, including search engines, DNA sequencing, stock market analysis, and robot locomotion, and their use is spreading rapidly. People who know the methods have their choice of rewarding jobs. This hands-on text opens these opportunities to computer science students with modest mathematical backgrounds. It is designed for final-year undergraduates and master's students with limited background in linear algebra and calculus. Comprehensive and coherent, it develops everything from basic reasoning to advanced techniques within the framework of graphical models. Students learn more than a menu of techniques, they develop analytical and problem-solving skills that equip them for the real world. Numerous examples and exercises, both computer based and theoretical, are included in every chapter. Resources for students and instructors, including a MATLAB toolbox, are available online.

    A software diskette provides an easy-to-use tool for students to derive probabilities for binomial.

    In studying number theory from such a perspective, mathematics majors are spared repetition and provided with new insights, while other students benefit from the consequent simplicity of the proofs for many theorems.Among the topics covered in this accessible, carefully designed introduction are multiplicativity-divisibility, including the fundamental theorem of arithmetic, combinatorial and computational number theory, congruences, arithmetic functions, primitive roots and prime numbers. Later chapters offer lucid treatments of quadratic congruences, additivity (including partition theory) and geometric number theory.Of particular importance in this text is the author's emphasis on the value of numerical examples in number theory and the role of computers in obtaining such examples. Exercises provide opportunities for constructing numerical tables with or without a computer. Students can then derive conjectures from such numerical tables, after which relevant theorems will seem natural and well-motivated..

    Switching from thin tailed to fat tailed distributions requires more than "changing the color of the dress." Traditional asymptotics deal mainly with either n=1 or n=∞, and the real world is in between, under the "laws of the medium numbers"-which vary widely across specific distributions. Both the law of large numbers and the generalized central limit mechanisms operate in highly idiosyncratic ways outside the standard Gaussian or Levy-Stable basins of convergence. A few examples: - The sample mean is rarely in line with the population mean, with effect on "na�ve empiricism," but can be sometimes be estimated via parametric methods. - The "empirical distribution" is rarely empirical. - Parameter uncertainty has compounding effects on statistical metrics. - Dimension reduction (principal components) fails. - Inequality estimators (Gini or quantile contributions) are not additive and produce wrong results. - Many "biases" found in psychology become entirely rational under more sophisticated probability distributions. - Most of the failures of financial economics, econometrics, and behavioral economics can be attributed to using the wrong distributions. This book, the first volume of the Technical Incerto, weaves a narrative around published journal articles.

    The novel approach taken here banishes determinants to the end of the book and focuses on the central goal of linear algebra: understanding the structure of linear operators on vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. For example, the book presents - without having defined determinants - a clean proof that every linear operator on a finite-dimensional complex vector space (or an odd-dimensional real vector space) has an eigenvalue. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. This second edition includes a new section on orthogonal projections and minimization problems. The sections on self-adjoint operators, normal operators, and the spectral theorem have been rewritten. New examples and new exercises have been added, several proofs have been simplified, and hundreds of minor improvements have been made throughout the text.

    He solidified his standing as the nation's foremost political forecaster with his near perfect prediction of the 2012 election. Silver is the founder and editor in chief of FiveThirtyEight.com. Drawing on his own groundbreaking work, Silver examines the world of prediction, investigating how we can distinguish a true signal from a universe of noisy data. Most predictions fail, often at great cost to society, because most of us have a poor understanding of probability and uncertainty. Both experts and laypeople mistake more confident predictions for more accurate ones. But overconfidence is often the reason for failure. If our appreciation of uncertainty improves, our predictions can get better too. This is the "prediction paradox": The more humility we have about our ability to make predictions, the more successful we can be in planning for the future.In keeping with his own aim to seek truth from data, Silver visits the most successful forecasters in a range of areas, from hurricanes to baseball, from the poker table to the stock market, from Capitol Hill to the NBA. He explains and evaluates how these forecasters think and what bonds they share. What lies behind their success? Are they good-or just lucky? What patterns have they unraveled? And are their forecasts really right? He explores unanticipated commonalities and exposes unexpected juxtapositions. And sometimes, it is not so much how good a prediction is in an absolute sense that matters but how good it is relative to the competition. In other cases, prediction is still a very rudimentary-and dangerous-science.Silver observes that the most accurate forecasters tend to have a superior command of probability, and they tend to be both humble and hardworking. They distinguish the predictable from the unpredictable, and they notice a thousand little details that lead them closer to the truth. Because of their appreciation of probability, they can distinguish the signal from the noise.