Probability and statistics Books

Book SynopsisDiscover football''s astonishing hidden rules in The Numbers Game by Chris Anderson and David Sally*Fully updated with a new World Cup chapter* Football has always been a numbers game: 4-4-2, the big number 9 and 3 points for a win. But what if up until now we''ve been focusing on the wrong numbers? What if the numbers that really matter, the ones that hold the key to winning matches, are actually 2.66, 53.4, 50/50, and 0 > 1? What if managers only make a 15% difference? What if Chelsea should have bought Darren Bent?In this incisive, myth-busting book, Chris Anderson, former goalkeeper turned football statistics guru, and David Sally, former baseball pitcher turned behavioural economist, show that every shred of knowledge we can gather can help us to love football and understand it even more. You''ll discover why stopping a goal is more valuable than scoring one, why corners should be taken short, and why it is better to improve yTrade ReviewDoes the impossible of making the beautiful game even more beautiful -- Malcolm GladwellA must-read . . . Chris Anderson and David Sally have the ability to see football in a way few have before them. Be warned: The Numbers Game will change the way you think about your favourite team or player, and change the way you watch the beautiful game. -- Billy Beane, General Manager of the Oakland A's, the subject of MoneyballA fascinating and stylish investigation into a rapidly developing way of understanding football -- Jonathan Wilson, author of Inverting the Pyramid: The History of Football TacticsWhether you are a traditionalist or a numbers nut you can enjoy this book. It's thorough, accessible, and devoid of the absolute truths so many on both sides of the debate peddle. -- Gabriele Marcotti, football broadcaster and authorIt is the book that could change the game forever * Times *You need to like football. Millions of people do. And they should rush to read this book immediately. The game they love will take on new depth, colour and subtlety -- Ed Smith * The Times *

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Book SynopsisThe phenomenal international bestseller that shows us how to stop trying to predict everything - and take advantage of uncertaintyWhat have the invention of the wheel, Pompeii, the Wall Street Crash, Harry Potter and the internet got in common? Why are all forecasters con-artists? Why should you never run for a train or read a newspaper? This book is all about Black Swans: the random events that underlie our lives, from bestsellers to world disasters. Their impact is huge; they''re impossible to predict; yet after they happen we always try to rationalize them. ''Taleb is a bouncy and even exhilarating guide ... I came to relish what he said, and even develop a sneaking affection for him as a person'' Will Self, Independent on Sunday''He leaps like some superhero of the mind'' Boyd Tonkin, IndependentTrade ReviewA fascinating study of how we are regularly taken for suckers by the unexpected * Guardian *Like the conversation of a raconteur ... hugely enjoyable - compelling * Financial Times *It has altered modern thinking * The Times *Confirms his status as a guru for every would-be Damien Hirst, George Soros and aspirant despot * Sunday Times *The Black Swan changed my view of how the world works -- Daniel Kahneman, author of Thinking, Fast and SlowGreat fun... brash, stubborn, entertaining, opinionated, curious, cajoling -- Stephen J. Dubner, co-author of FreakonomicsThe most prophetic voice of all * GQ *

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Book SynopsisHow do you remember more and forget less?How can you earn more and become more creative just by moving house?And how do you pack a car boot most efficiently?This is your shortcut to the art of the shortcut.Mathematics is full of better ways of thinking, and with over 2,000 years of knowledge to draw on, Oxford mathematician Marcus du Sautoy interrogates his passion for shortcuts in this fresh and fascinating guide. After all, shortcuts have enabled so much of human progress, whether in constructing the first cities around the Euphrates 5,000 years ago, using calculus to determine the scale of the universe or in writing today's algorithms that help us find a new life partner.As well as looking at the most useful shortcuts in history such as measuring the circumference of the earth in 240 BC to diagrams that illustrate how modern GPS works Marcus also looks at how you can use shortcuts in investing or how to learn a musical instrument to memory techniques. He talks to, among many, the Trade Review‘enjoyably clever …with vividly illustrated chapters about the real-world applications of algebra, geometry, probability theory…It’s Du Sautoy, in the end, who provides the wisest commentary’ Steven Poole, Guardian ‘If you thought Maths was all about long stuff, like long division and long multiplication and taking a long, long time to figure things out, Marcus du Sautoy shows that it's just the opposite. Full of humour, stories and the lightest of touches, this is a sight-seeing tour of some of the world's greatest neat dodges, unexpected turns and useful cut-throughs. Prepare to be caught short’ Michael Rosen ‘This book will change the way you look at the world. It's chock full of stories, ideas and clever tricks – I loved it. Marcus is a maestro at making big ideas come alive – he deserves his place alongside Richard Dawkins, E. O. Wilson and Carlo Rovelli in the pantheon of great modern science writers’ Rohan Silva, CEO and founder of Second Home ‘If mathematics has proved anything, it is that shortcuts can change the world. Marcus du Sautoy has come up with a smart, well written and entertaining guide to the connecting tunnels, underpasses and other tricks to traverse the trials of everyday life’ Roger Highfield, author, broadcaster and Science Director at the Science Museum ‘The joy of du Sautoy’s book isn’t really the art of the real-world shortcut at all. It is the romp through mathematical ideas, from place value to non Euclidean geometry to probability theory…There are vivid historical examples of scientists and others using mathematical ideas to solve problems’ Tim Harford, Financial Times

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Book SynopsisMaking good decisions under conditions of uncertainty - which is the norm - requires a sound appreciation of the way random chance works. As analysis and modelling of most aspects of the world, and all measurement, are necessarily imprecise and involve uncertainties of varying degrees, the understanding and management of probabilities is central to much work in the sciences and economics. In this Very Short Introduction, John Haigh introduces the ideas of probability and different philosophical approaches to probability, and gives a brief account of the history of development of probability theory, from Galileo and Pascal to Bayes, Laplace, Poisson, and Markov. He describes the basic probability distributions, and goes on to discuss a wide range of applications in science, economics, and a variety of other contexts such as games and betting. He concludes with an intriguing discussion of coincidences and some curious paradoxes. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.Trade ReviewAn excellent and provocative introduction to a fascinating and underappreciated subject. * Mathematical Gazette *Table of Contents1. Fundamentals ; 2. The workings of probability ; 3. Historical sketch ; 4. Chance experiments ; 5. Making sense of probabilities ; 6. Games people play ; 7. Applications in science and operations research ; 8. Other applications ; 9. Curiosities and dilemmas ; Appendix - Answers to questions posed

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Book SynopsisWe are the safest humans who ever lived - the statistics prove it. And yet the media tells a different story with its warnings and scare stories. How is it possible that anxiety has become the stuff of daily life?In this ground-breaking, compulsively readable book, Dan Gardner shows how our flawed strategies for perceiving risk influence our lives, often with unforeseen and sometimes-tragic consequences. He throws light on our paranoia about everything from paedophiles to terrorism and reveals how the most significant threats are actually the mundane risks to which we pay little attention.Speaking to psychologists and scientists, as well as looking at the influence of the media and politicians, Gardner uncovers one of the central puzzles of our time: why are the safest people in history living in a culture of fear?Trade ReviewExcellent ... Gardner analyses everything from the media's predilection for irrational scare stories to the cynical use of fear by politicians pushing a particular agenda ... A cheery corrective to modern paranoia * Economist *Terrific ... exceptionally good - has the clarity of Malcolm Gladwell * Evening Standard *Enlivening ... a fascinating insight into the peculiar and devastating nature of human fear * Sunday Telegraph *Stimulating ... where writers such as Richard Dawkins, Christopher Hitchens and Francis Wheen have been content largely to enumerate the errors of less rational men and women, Dan Gardner has collated part of what we need to diagnose the problem * Independent on Sunday *Beautifully observed * Observer *

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Book SynopsisTHE CLASSIC GUIDE, NOW FULLY REVISED AND UPDATEDWhy do we need Statistics?What do terms like ''dispersion'', ''correlation'', ''normal distribution'' and ''significance'' actually mean?How can I learn how to think statistically?This bestselling introduction is for anyone who wants to know how statistics works and the powerful ideas behind it. Teaching through words and diagrams instead of requiring you to do complex calculations, it assumes no expert knowledge and makes the subject accessible even to readers who consider themselves non-mathematical. This clear and informative ''tutorial in print'' includes questions for you to respond to in the light of what you have read so far, ensuring your developing ability to think statistically.

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Book SynopsisThis book demonstrates the importance of computer-generated statistical analyses in behavioral science research, particularly those using the R software environment. Statistical methods are being increasingly developed and refined by computer scientists, with expertise in writing efficient and elegant computer code. Unfortunately, many researchers lack this programming background, leaving them to accept on faith the black-box output that emerges from the sophisticated statistical models they frequently use. Building on the author’s previous volume, Linear Models in Matrix Form, this text bridges the gap between computer science and research application, providing easy-to-follow computer code for many statistical analyses using the R software environment. The text opens with a foundational section on linear algebra, then covers a variety of advanced topics, including robust regression, model selection based on bias and efficiency, nonlinear models and optimization routines, generalized linear models, and survival and time-series analysis. Each section concludes with a presentation of the computer code used to illuminate the analysis, as well as pointers to packages in R that can be used for similar analyses and nonstandard cases. The accessible code and breadth of topics make this book an ideal tool for graduate students or researchers in the behavioral sciences who are interested in performing advanced statistical analyses without having a sophisticated background in computer science and mathematics.Table of ContentsLinear Equations.- Least Squares Estimation.- Linear Regression.- Eigen Decomposition.- Singular Value Decomposition.- Generalized Least Squares Estimation.- Robust Regression.- Model Selection and Biased Estimation.- Cubic Splines and Additive Models.- Nonlinear Regression and Optimization.- Generalized Linear Models.- Survival Analysis.- Time Series Analysis.- Mixed Effects Models.

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This book sheds new light on stochastic calculus, the branch of mathematics that is most widely applied in financial engineering and mathematical finance. The first book to introduce pathwise formulae for the stochastic integral, it provides a simple but rigorous treatment of the subject, including a range of advanced topics. The book discusses in-depth topics such as quadratic variation, Ito formula, and Emery topology. The authors briefly addresses continuous semi-martingales to obtain growth estimates and study solution of a stochastic differential equation (SDE) by using the technique of random time change. Later, by using Metivier–Pellaumail inequality, the solutions to SDEs driven by general semi-martingales are discussed. The connection of the theory with mathematical finance is briefly discussed and the book has extensive treatment on the representation of martingales as stochastic integrals and a second fundamental theorem of asset pricing. Intended for undergraduate- and beginning graduate-level students in the engineering and mathematics disciplines, the book is also an excellent reference resource for applied mathematicians and statisticians looking for a review of the topic.

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Book SynopsisWhether you’re a student or an adult looking to refresh your knowledge, Barron’s Painless Statistics provides review and practice in an easy, step-by-step format.An essential resource for: Virtual learning Homeschool Learning pods Supplementing classes/in-person learning Inside you’ll find: Clear examples for all topics, including data and distributions, basic probability, confidence intervals, bivariate statistics, and much more Diagrams, charts, and instructive math illustrations Painless tips, common pitfalls, and informative sidebars Math talk boxes that translate complex “math speak” into easy-to-understand language Brain Tickler quizzes throughout each chapter to test your progress

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Book SynopsisModern statistics is very different from the dry and dusty discipline of the popular imagination. In its place is an exciting subject which uses deep theory and powerful software tools to shed light and enable understanding. And it sheds this light on all aspects of our lives, enabling astronomers to explore the origins of the universe, archaeologists to investigate ancient civilisations, governments to understand how to benefit and improve society, and businesses to learn how best to provide goods and services. Aimed at readers with no prior mathematical knowledge, this Very Short Introduction explores and explains how statistics work, and how we can decipher them. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.Table of ContentsPreface ; 1. Surrounded by Statistics ; 2. Simple descriptions ; 3. Collecting good data ; 4. Probability ; 5. Estimation and inference ; 6. Statistical models and methods ; 7. Statistical computing ; Further reading ; Index

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Book SynopsisPreface Statistics is seldom the most eagerly anticipated course of a business student. Our goal in writing this casebook and the companion volume (Business Analysis Using Regression) was to change that impression by showing how statistics yields insights and answers interesting business questions.Trade Review"The manuscripts are divided into "classes" which tackle various statistical concepts. Material becomes increasingly complex as the data in later sections exhibit multiple deviations from ideal conditions. The casebooks use a combination of explanatory text and software output to guide the student. Almost no mathematics appears in these volumes; the authors make traditional texts available to their students who are curious about the technical details...I anticipate students will wholeheartedly endorse the FSW casebooks. The material is easy to digest as, for instance, the authors cleverly interweave probability, the standard error of the mean, and control charts. The casebooks effectively relay the message that statistics is relevant and doable. Ideally, that is the message that should be sent in all introductory business statistics courses." Marlene Smith, University of Colorado-DenverTable of ContentsOverview and Foundations * Statistical Summaries of Data * Sources of Variation * Standard Error * Confidence Intervals * Sampling * Making Decisions * Designing Tests for Better Comparisons * Confounding Effects in Tests: A Case Study * Covariance, Correlation, and Portfolios * A Preview of Regression

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Book SynopsisA leading data visualisation expert explores the negative—and positive-influences that charts have on our perception of truthTrade Review"[Alberto Cairo's] book reminds readers not to infer too much from a chart, especially when it shows them what they already wanted to see. Mr Cairo has sent a copy to the White House." -- The Economist

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Book SynopsisWhy is it that incredibly unlikely phenomena actually happen quite regularly and why should we, in fact, expect such things to happen? Here, in this highly original book - aimed squarely at anyone with an interest in coincidences, probability or gambling - eminent statistician David Hand answers this question by weaving together various strands of probability into a unified explanation, which he calls the improbability principle.This is a book that will appeal not only to those who love stories about startling coincidences and extraordinarily rare events, but also to those who are interested in how a single bold idea links areas as diverse as gambling, the weather, airline disasters and creative writing as well as the origin of life and even the universe. The Improbability Principle will change your perspective on how the world works and tell you what the Bible code and Shakespeare have in common, how to win the lottery, why Apple''s song shuffling was made less random to seem more random. Oh and why lightning does in fact strike twice...Trade ReviewA hugely entertaining eye-opener about how misuse of statistics can skew our view of the world * Daily Mail *Lively and lucid . . . an intensely useful (as well as a remarkably entertaining) book . . . * Salon *In my experience, it is very rare to find a book that is both erudite and entertaining. Yet The Improbability Principle is such a book. Surely this cannot be due to chance alone! -- Hal Varian, Google’s Chief EconomistAn elegant, astoundingly clear and enjoyable combination of subtle statistical thinking and real-world events. -- Andrew Dilnot, co-author of 'The Numbers Game'As someone who happened to meet his future wife on a plane, on an airline he rarely used, I wholeheartedly endorse David Hand’s fascinating guide to improbability, a subject which affects the lives of all, yet until now has lacked a coherent exposition of its underlying principles. -- Gordon Woo, catastrophist at Risk Management Solutions

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Book SynopsisA First Course in Ergodic Theory provides readers with an introductory course in Ergodic Theory. This textbook has been developed from the authorsâ own notes on the subject, which they have been teaching since the 1990s. Over the years they have added topics, theorems, examples and explanations from various sources. The result is a book that is easy to teach from and easy to learn from â designed to require only minimal prerequisites.Features Suitable for readers with only a basic knowledge of measure theory, some topology and a very basic knowledge of functional analysis Perfect as the primary textbook for a course in Ergodic Theory Examples are described and are studied in detail when new properties are presented. Trade Review"A First Course in Ergodic Theory by Dajani and Kalle provides not only a crystal clear introduction to the core of ergodic theory, but also goes down paths previously accessible only through the research literature. The book covers ergodic theorems, invariant measures, entropy and the variational principle. But it also covers piecewise monotone interval maps, Perron-Frobenius operators, natural extensions, and the useful lemma of Knopp. Another theme is the theory of conservative nonsingular and infinite measure preserving transformations. All of this is illustrated via numerous examples from (not necessarily regular) continued fractions and other number expansions, the authors’ specialty. Throughout the book, the proofs patiently explain details often ignored. An excellent appendix provides a reference to needed results from topology, measure theory, probability and functional analysis."– E. Arthur (Robbie) Robinson, Jr., Professor of Mathematics at George Washington University and co-author of The Mathematics of Politics"This textbook is a delightful introduction to Ergodic Theory. It starts at a basic level, giving intuitive explanations and motivations, and concludes with more advanced topics such as variational principle and infinite ergodic theory. The style is very crisp, and many of the results are proved. Examples which are primarily taken from number theory run as a red thread through the manuscript. This makes this textbook quite different from other classic textbooks on the subject. It’s very easy to build an advanced UG or a postgraduate lecture course around this material."– Sebastian van Strien, Imperial College LondonTable of ContentsPreface. Author Bios. 1. Measure preservingness and basic examples. 1.1. What is Ergodic Theory. 1.2. Measure Preserving Transformations. 1.3. Basic Examples. 2. Recurrence and Ergodicity. 2.1. Recurrence. 2.2. Ergodicity. 2.3. Examples of Ergodic Transformations. 3. The Pointwise Ergodic Theorem and its consequences. 3.2. Normal Numbers. 3.3. Characterization of Irreducible Markov Chains. 3.4. Mixing. 4. More Ergodic Theorem. The mean Ergodic Theorem. 4.2. The Hurewicz Erogdic Theorem. 5. Measure Preserving Isomorphisms. 5.2. Factor Maps. 5.3. Natural Extensions. 6. The Perron–Frobenius Operator. 6.1. Absolutely Continuous Invariants Measures. 6.2. Exactness. Densities for Piecewise Monotnoe Interval Maps. 7. Invariant Measures for Continuous Transformations. 7.1. Existence. 7.2. Unique Ergodicity and Inform Distributions. 7.3. Some Topological Dynamics. 8. Continued Fractions. 8.1. Basic Properties of Regular Continue Fractions. 8.2. Ergodic Properties of Gauss Map. 8.3. Natural Extension and the Doeblin–Lenstra Conjecture. 8.4. Other Continue Fraction Transformation. 9. Entropy. 9.1. Randomness and Information. 9.2. Definitions and Properties. Calculation of Entropy and Examples. 9.4. The Shannon–McMillan–Breiman Theorem. 9.5. Lochs’ Theorem. 10. The Variational Principle. 10.1 Topological Entropy. 10.2. Main Theorem. 10.3. Measures of Maximal Entropy. 11. Infinite Ergodic Theory. 11.1 Examples of Infinite Measure Dynamical Systems. 11.2. Conservative and Dissipative Part. 11.3. Induced Systems. 11.4. Jump Transformations. 11.5. Ergodic Theorem for Infinite Measure Systems. 12. Appendix. 12.1. Topology. 12.2. Measure Theory. 12.3 Lebesgue Spaces. 12.4. Lebesgue Integration and Convergence Results. 12.5. Hilbert’s Spaces. 12.6. Borel Measures on Compact Metric Spaces. 12.7. Functions of Bounded Variation. Bibliography. Index.

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Book SynopsisThis textbook shows how to bring theoretical concepts from finance and econometrics to the data. Focusing on coding and data analysis with Python, we show how to conduct research in empirical finance from scratch. We start by introducing the concepts of tidy data and coding principles using pandas, numpy, and plotnine. Code is provided to prepare common open-source and proprietary financial data sources (CRSP, Compustat, Mergent FISD, TRACE) and organize them in a database. We reuse these data in all the subsequent chapters, which we keep as self-contained as possible. The empirical applications range from key concepts of empirical asset pricing (beta estimation, portfolio sorts, performance analysis, Fama-French factors) to modeling and machine learning applications (fixed effects estimation, clustering standard errors, difference-in-difference estimators, ridge regression, Lasso, Elastic net, random forests, neural networks) and portfolio optimization techniques.Key Feature

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Book SynopsisDoes the subject of data analysis make you dizzy? This book features introduction to exploratory data analysis, the lowdown on collecting, cleaning, and organizing data, everything you need to know about interpreting data using common software and programming languages. It helps you to identify valid, useful, and understandable patterns in data.Table of ContentsIntroduction 1 Part I: Introducing Big Data Statistics 7 Chapter 1: What Is Big Data and What Do You Do With It? 9 Chapter 2: Characteristics of Big Data: The Three Vs 19 Chapter 3: Using Big Data: The Hot Applications 27 Chapter 4: Understanding Probabilities 41 Chapter 5: Basic Statistical Ideas 57 Part II: Preparing and Cleaning Data 81 Chapter 6: Dirty Work: Preparing Your Data for Analysis 83 Chapter 7: Figuring the Format: Important Computer File Formats 99 Chapter 8: Checking Assumptions: Testing for Normality 107 Chapter 9: Dealing with Missing or Incomplete Data 119 Chapter 10: Sending Out a Posse: Searching for Outliers 129 Part III: Exploratory Data Analysis (EDA) 141 Chapter 11: An Overview of Exploratory Data Analysis (EDA) 143 Chapter 12: A Plot to Get Graphical: Graphical Techniques 155 Chapter 13: You’re the Only Variable for Me: Univariate Statistical Techniques 173 Chapter 14: To All the Variables We’ve Encountered: Multivariate Statistical Techniques 191 Chapter 15: Regression Analysis 215 Chapter 16: When You’ve Got the Time: Time Series Analysis 243 Part IV: Big Data Applications 269 Chapter 17: Using Your Crystal Ball: Forecasting with Big Data 271 Chapter 18: Crunching Numbers: Performing Statistical Analysis on Your Computer 297 Chapter 19: Seeking Free Sources of Financial Data 319 Part V: The Part of Tens 331 Chapter 20: Ten (or So) Best Practices in Data Preparation 333 Chapter 21: Ten (or So) Questions Answered by Exploratory Data Analysis (EDA) 339 Index 349

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Book SynopsisMany of the concepts and terminology surrounding modern causal inference can be quite intimidating to the novice. Judea Pearl presents a book ideal for beginners in statistics, providing a comprehensive introduction to the field of causality.Trade Review"Despite the fact that quite a few high-quality books on the topic of causal inference have recently been published, this book clearly fills an important gap: that of providing a simple and clear primer...Use of counterfactuals [in the final chapter] is elegantly linked to the structural causal models outlined in the previous chapters...[while]intriguing examples are used to introduce and illustrate the main concepts and methods...Several thought provoking study questions, in the form of exercises, are given throughout the presentation, and they can be very helpful for a better understanding of the material and looking further into the subtleties of the concepts introduced. In summary, there is no doubt that a discussion of the basic ideas in causal inference should be included in all introductory courses of statistics. This book could serve as a very useful companion to the lectures." (Mathematical Reviews/MathSciNet April 2017)Table of ContentsAbout the Authors ix Preface xi List of Figures xv About the Companion Website xix 1 Preliminaries: Statistical and Causal Models 1 1.1 Why Study Causation 1 1.2 Simpson’s Paradox 1 1.3 Probability and Statistics 7 1.3.1 Variables 7 1.3.2 Events 8 1.3.3 Conditional Probability 8 1.3.4 Independence 10 1.3.5 Probability Distributions 11 1.3.6 The Law of Total Probability 11 1.3.7 Using Bayes’ Rule 13 1.3.8 Expected Values 16 1.3.9 Variance and Covariance 17 1.3.10 Regression 20 1.3.11 Multiple Regression 22 1.4 Graphs 24 1.5 Structural Causal Models 26 1.5.1 Modeling Causal Assumptions 26 1.5.2 Product Decomposition 29 2 Graphical Models and Their Applications 35 2.1 Connecting Models to Data 35 2.2 Chains and Forks 35 2.3 Colliders 40 2.4 d-separation 45 2.5 Model Testing and Causal Search 48 3 The Effects of Interventions 53 3.1 Interventions 53 3.2 The Adjustment Formula 55 3.2.1 To Adjust or not to Adjust? 58 3.2.2 Multiple Interventions and the Truncated Product Rule 60 3.3 The Backdoor Criterion 61 3.4 The Front-Door Criterion 66 3.5 Conditional Interventions and Covariate-Specific Effects 70 3.6 Inverse Probability Weighing 72 3.7 Mediation 75 3.8 Causal Inference in Linear Systems 78 3.8.1 Structural versus Regression Coefficients 80 3.8.2 The Causal Interpretation of Structural Coefficients 81 3.8.3 Identifying Structural Coefficients and Causal Effect 83 3.8.4 Mediation in Linear Systems 87 4 Counterfactuals and Their Applications 89 4.1 Counterfactuals 89 4.2 Defining and Computing Counterfactuals 91 4.2.1 The Structural Interpretation of Counterfactuals 91 4.2.2 The Fundamental Law of Counterfactuals 93 4.2.3 From Population Data to Individual Behavior – An Illustration 94 4.2.4 The Three Steps in Computing Counterfactuals 96 4.3 Nondeterministic Counterfactuals 98 4.3.1 Probabilities of Counterfactuals 98 4.3.2 The Graphical Representation of Counterfactuals 101 4.3.3 Counterfactuals in Experimental Settings 103 4.3.4 Counterfactuals in Linear Models 106 4.4 Practical Uses of Counterfactuals 107 4.4.1 Recruitment to a Program 107 4.4.2 Additive Interventions 109 4.4.3 Personal Decision Making 111 4.4.4 Sex Discrimination in Hiring 113 4.4.5 Mediation and Path-disabling Interventions 114 4.5 Mathematical Tool Kits for Attribution and Mediation 116 4.5.1 A Tool Kit for Attribution and Probabilities of Causation 116 4.5.2 A Tool Kit for Mediation 120 References 127 Index 133

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Book SynopsisThis class-tested textbook will provide in-depth coverage of the fundamentals of machine learning, with an exploration of applications in information security. The book will cover malware detection, cryptography, and intrusion detection. The book will be relevant for students in machine learning and computer security courses.

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Book SynopsisDo you need to gain confidence with handling numbers and formulae? Do you want a clear, step-by-step guide to the key concepts and principles of statistics? Nearly all aspects of our lives can be subject to statistical analysis. Statistics: An Introduction shows you how to interpret, analyze and present figures.Assuming minimal knowledge of maths and using examples from a wide variety of everyday contexts, this book makes often complex concepts and techniques easy to get to grips with. This new edition has been fully updated.Whether you want to understand the statistics that you are bombarded with every day or are a student or professional coming to statistics from a wide range of disciplines, Statistics: An Introduction covers it all.

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Book SynopsisThis second edition textbook offers a practical introduction to probability for undergraduates at all levels with different backgrounds and views towards applications. Calculus is a prerequisite for understanding the basic concepts, however the book is written with a sensitivity to students’ common difficulties with calculus that does not obscure the thorough treatment of the probability content. The first six chapters of this text neatly and concisely cover the material traditionally required by most undergraduate programs for a first course in probability. The comprehensive text includes a multitude of new examples and exercises, and careful revisions throughout. Particular attention is given to the expansion of the last three chapters of the book with the addition of one entirely new chapter (9) on ’Finding and Comparing Estimators.’ The classroom-tested material presented in this second edition forms the basis for a second course introducing mathematical statistics.Table of ContentsProbability Space.- Conditional probabilities.- Discrete random variables.- Binomial random variables.- Poisson random variables.- Simulations of discrete random variables.- Combinatorics.- Continuous random variables.- The sample average and sample.- Estimating and testing proportions.- Estimating and testing means.- Small samples.- Chi-squared tests.- Design of experiments.- The cumulative distribution function.- Continuous joint distributions.- Covariance and independence.- Conditional distribution and expectation.- The bivariate normal distribution.- Sums of Bernoulli random variables.- Coupling random variables.- The moment generating function.- The chi-squared, Student and F distributions.- Sampling from a normal distribution.- Finding estimators.- Comparing estimators.- Best unbiased estimators.- Bayes’ estimator.- Multiple linear regression.- List of common discrete distributions.- List of common continuous distributions.- Further reading.- Normal table.- Student table.- Chi-squared table.- Index.

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Book SynopsisOtt and Longnecker's AN INTRODUCTION TO STATISTICAL METHODS AND DATA ANALYSIS, Seventh Edition, provides a broad overview of statistical methods for advanced undergraduate and graduate students from a variety of disciplines who have little or no prior course work in statistics. The authors teach students to solve problems encountered in research projects, to make decisions based on data in general settings both within and beyond the university setting, and to become critical readers of statistical analyses in research papers and news reports. The first eleven chapters present material typically covered in an introductory statistics course, as well as case studies and examples that are often encountered in undergraduate capstone courses. The remaining chapters cover regression modeling and design of experiments.Table of ContentsPART 1: INTRODUCTION. 1. Statistics and the Scientific Method. Introduction. Why Study Statistics? Some Current Applications of Statistics. A Note to the Student. Summary. Exercises. PART 2: COLLECTING DATA. 2. Using Surveys and Scientific Studies to Collect Data. Introduction and Abstract of Research Study. Observational Studies. Sampling Designs for Surveys. Experimental Studies. Designs for Experimental Studies. Research Study: Exit Polls versus Election Results. Summary. Exercises. PART 3: SUMMARIZING DATA. 3. Data Description. Introduction and Abstract of Research Study. Calculators, Computers, and Software Systems. Describing Data on a Single Variable: Graphical Methods. Describing Data on a Single Variable: Measures of Central Tendency. Describing Data on a Single Variable: Measures of Variability. The Boxplot. Summarizing Data from More Than One Variable: Graphs and Correlation. Research Study: Controlling for Student Background in the Assessment of Teaching. Summary and Key Formulas. Exercises. 4. Probability And Probability Distributions. Introduction and Abstract of Research Study. Finding the Probability of an Event. Basic Event Relations and Probability Laws. Conditional Probability and Independence. Bayes' Formula. Variables: Discrete and Continuous. Probability Distributions for Discrete Random Variables. Two Discrete Random Variables: The Binomial and the Poisson. Probability Distributions for Continuous Random Variables. A Continuous Probability Distribution: The Normal Distribution. Random Sampling. Sampling Distributions. Normal Approximation to the Binomial. Evaluating Whether or Not a Population Distribution Is Normal. Research Study: Inferences about Performance Enhancing Drugs among Athletes. Minitab Instructions. Summary and Key Formulas. Exercises. PART 4: ANALYZING DATA, INTERPRETING THE ANALYSES, AND COMMUNICATING RESULTS. 5. Inferences about Population Central Values. Introduction and Abstract of a Research Study. Estimation of ��. Choosing the Sample Size for Estimating ��. A Statistical Test for ��. Choosing the Sample Size for ��. The Level of Significance of a Statistical Test. Inferences about �� for a Normal Population, �� Unknown. Inferences about �� when Population in Nonnormal and n is small: Bootstrap Methods. Inferences about the Median. Research Study: Percent Calories from Fat. Summary and Key Formulas. Exercises. 6. Inferences Comparing Two Population Central Values. Introduction and Abstract of a Research Study. Inferences about ��1 ��� ��2: Independent Samples. A Nonparametric Alternative: The Wilcoxon Rank Sum Test. Inferences about ��1 ��� ��2: Paired Data. A Nonparametric Alternative: The Wilcoxon Signed-Rank Test. Choosing Sample Sizes for Inferences about ��1 ��� ��2. Research Study: Effects of Oil Spill on Plant Growth. Summary. Exercises. 7. Inferences about Population Variances. Introduction and Abstract of a Research Study. Estimation and Tests for a Population Variance. Estimation and Tests for Comparing Two Population Variances. Tests for Comparing t > 2 Population Variances. Research Study: Evaluation of Methods for Detecting E. coli. Summary and Key Formulas. Exercises. 8. Inferences About More Than Two Population Central Values Introduction and Abstract of a Research Study. A Statistical Test About More Than Two Population Means: An Analysis of Variance. The Model for Observations in a Completely Randomized Design. Checking on the AOV Conditions. An Alternative Analysis: Transformations of the Data. A Nonparametric Alternative: The Kruskal-Wallis Test. Research Study: Effect on Timing on the Treatment of Port-Wine Stains with Lasers. Summary and Key Formulas. Exercises. 9. Multiple Comparisons. Introduction and Abstract of Research Study. Linear Contrasts. Which Error Rate Is Controlled? Fisher's Least Significant Difference. Tukey's W Procedure. Student-Neuman-Keuls Procedure. Dunnett's Procedure: Comparison of Treatments to a Control. Scheff��'s S Method. A Nonparametric Multiple-Comparison Procedure. Research Study: Are Interviewers' Decisions Affected by Different Handicap Types? Summary and Key Formulas. Exercises. 10. Categorical Data. Introduction and Abstract of Research Study. Inferences about a Population Proportion ���. Inferences about the Difference between Two Population Proportions, ���1 ��� ���2. Inferences about Several Proportions: Chi-Square Goodness-of-Fit Test. Tests for Independence and Homogeneity. Measuring Strength of Relaxation. Odds and Odd Ratios. Combining Sets of 2 ��� 2 Contingency Tables (optional). Research Study: Does Gender Bias Exist in the Selection of Students for Vocational Education? Summary and Key Formulas. Exercises. PART 5: ANALYZING DATA: REGRESSION METHODS AND MODEL BUILDING. 11. Linear Regression and Correlation. Introduction and Abstract of Research Study. Estimating Model Parameters. Inferences about Regression Parameters. Predicting New y Values Using Regression. Examining Lack of Fit in Linear Regression. The Inverse Regression Problem (Calibration). Correlation. Research Study: Two Methods for Detecting E. coli. Summary and Key Formulas. Exercises. 12. Multiple Regression and the General Linear Model. Introduction and Abstract of Research Study. The General Linear Model. Estimating Multiple Regression Coefficients. Inferences in Multiple Regression. Testing a Subset of Regression Coefficients. Forecasting Using Multiple Regression. Comparing the Slopes of Several Regression Lines. Logistic Regression. Some Multiple Regression Theory (Optional). Research Study: Designing an Electric Drill. Summary and Key Formulas. Exercises. 13. Further Regression Topics. Introduction and Abstract of Research Study. Selecting the Variables (Step 1). Formulating the Model (Step 2). Checking Model Assumptions (Step 3). Research Study: Construction Costs for Nuclear Power Plants. Summary and Key Formulas. Exercises. PART 6: DESIGN OF EXPERIMENTS AND ANALYSIS OF VARIANCE. 14. Analysis of Variance for Completely Randomized Designs. Introduction and Abstract of Research Study. Completely Randomized Design with Single Factor. Factorial Treatment Structure. Factorial Treatment Structures with an Unequal Number of Replications. Estimation of Treatment Differences and Comparisons of Treatment Means. Determining the Number of Replications. Research Study: Development of a Low-Fat Processed Meat. Summary and Key Formulas. Exercises. 15. Analysis of Variance for Blocked Designs. Introduction and Abstract of Research Study. Randomized Complete Block Design. Latin Square Design. Factorial Treatment Structure in a Randomized Complete Block Design. A Nonparametric Alternative���Friedman's Test. Research Study: Control of Leatherjackets. Summary and Key Formulas. Exercises. 16. Analysis of Covariance. Introduction and Abstract of Research Study. A Completely Randomized Design with One Covariate. The Extrapolation Problem. Multiple Covariates and More Complicated Designs. Research Study: Evaluations of Cool-Season Grasses for Putting Greens. Summary. Exercises. 17. Analysis of Variance for Some Fixed-, Random-, and Mixed-Effects Models. Introduction and Abstract of Research Study. A One-Factor Experiment with Random Treatment Effects. Extensions of Random-Effects Models. Mixed-Effects Models. Rules for Obtaining Expecting Mean Squares. Nested Factors. Research Study: Factors Affecting Pressure Drops Across Expansion Joints . Summary. Exercises. 18. Split-Plot, Repeated Measures, and Crossover Designs. Introduction and Abstract of Research Study. Split-Plot Designs. Single-Factor Experiments with Repeated Measures on One of the Factors. Two-Factor Experiments with Repeated Measures on One of the Factors. Crossover Design. Research Study: Effects of Oil Spill on Plant Growth. Summary. Exercises. 19. Analysis of Variance for Some Unbalanced Designs. Introduction and Abstract of Research Study. A Randomized Block Design with One or More Missing Observations. A Latin Square Design with Missing Data. Balanced Incomplete Block (BIB) Designs. Research Study: Evaluation of the Consistency of Property Assessment. Summary and Key Formulas. Exercises. PART 7: COMMUNICATING AND DOCUMENTING THE RESULTS OF ANALYSES 20. Communicating and Documenting the Results of a Study or Experiment. Introduction. The Difficulty of Good Communication. Communication Hurdles: Graphical Distortions. Communication Hurdles: Biased Samples. Communication Hurdles: Sample Size. The Statistical Report. Documentation and Storage of Results. Summary. Exercises.

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Book SynopsisHow does chance enter our world? And why is so much not predictable?In an understandable, exciting and amusing narrative, the author takes us into the world of chemistry, quantum physics and biology. Touching on astronomy and philosophy, we witness a rewarding journey of discovery. In the process, he develops a completely new view of chance based on the laws of nature. Here, the omnipresent non-equilibrium plays an extremely decisive role, because it generates the complex structures in our world. Finally, on this basis, he presents an equally simple and captivating hypothesis on the nature of time.This non-fiction book provides a deep insight into the fascination of research, the agonizing search for fundamental understanding, and the struggle for scientific knowledge.Table of ContentsChance takes its course.- Chance is everywhere.- Creativity is chance in the brain.- "Balance is good, non-balance is bad" - is it true?- Almost despairing of science.- The birth of chance in complex systems.- What is there when time flows, and where does it flow to?- Our perception of time.

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Book SynopsisEverything a student needs to ensure exam success Written by Chief examiners and experienced teachers. Revised and enhanced following user feedback on the 2001 Heinemann edition. Practice exam papers for foundation and higher, exactly matched to the new specification. Three revision exercises, featuring past exam questions, consolidate learning on groups of topics. examzone section gives tips, tests and techniques for exam preparation and the new controlled assessment.

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Book SynopsisTrade ReviewThe human mind soaks up the images and narratives conveyed by the press, but they are a highly nonrandom sample of reality: the lurid, the sudden, the photogenic. Smil's title says it all: to understand the world, you need to follow the trendlines, not the headlines. This is a compelling, fascinating, and most important, realistic portrait of the world and where it's going -- Steven PinkerThe best book to read to better understand our world. Once in a while a book comes along that helps us see our planet more clearly. By showing us numbers about science, health, green technology and more, Smil's book does just that. It should be on every bookshelf! -- Linda Yueh, author of The Great EconomistsImportant -- Mark Zuckerberg, on EnergyOne of the world's foremost thinkers on development history and a master of statistical analysis . . . The nerd's nerd * Guardian *A book for anyone confused by statistics or dubious of data in a world where numbers seem to mean everything and nothing. Vaclav Smil's new book reveals why diesel isn't as bad as you think, how much food is really being wasted, what actually makes people happy, and much more. * BBC Science Focus magazine *Outstanding perspectives on the world we live in providing context on mankind's challenges ranging from demographics through globalization, innovation and the environment -- Sarah Riopelle, Senior portfolio manager at RBC Global Asset Management * Bloomberg, 'Best Books of 2022' *

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Book SynopsisTrade Review"Sports fans will learn much from probability theory and statistical models as they abandon empty clichés (time to throw momentum out of the informed fan's lexicon) and confront institutionalized injustices (such as those built into the protocols for selecting a national champion in college football and for seeding the NCAA's basketball tournament). A rare fusion of sports enthusiasm and numerical acumen." * Booklist *"Who is Wayne Winston? Maybe we should begin by telling you who he is not. He is not some barstool fan or uninformed sportswriter who fuels his opinions with information gleaned from SportsCenter highlights or newspaper box scores. He is a professor of decision sciences at Indiana University's Kelley School of Business, and until this year was the statistical guru for the Dallas Mavericks. He is author of the book Mathletics, which explains what statistics really tell us about sports."---Ken Berger, CBSSports.com"[A] terrific read for anyone trying to model markets statistically and make trading decisions based on statistical data. . . . Reading Winston's book is a mind-opening experience."---Brenda Jubin, Reading the Markets blog"[Huge] and highly interesting."---Mathematics Magazine, Paul J. Campbell

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Book SynopsisLeonard Mlodinow''s The Drunkard''s Walk: How Randomness Rules Our Lives is an exhilarating, eye-opening guide to understanding our random world.Randomness and uncertainty surround everything we do. So why are we so bad at understanding them? The same tools that help us understand the random paths of molecules can be applied to the randomness that governs so many aspects of our everyday lives, from winning the lottery to road safety, and reveals the truth about the success of sporting heroes and film stars, and even how to make sense of a blood test.The Drunkard''s Walk reveals the psychological illusions that prevent us understanding everything from stock-picking to wine-tasting - read it, or risk becoming another victim of chance.''A wonderfully readable guide to how the mathematical laws of randomness affect our lives'' Stephen Hawking, author of A Brief History of TimeTrade Review'Mlodinow writes in a breezy style, interspersing probabilistic mind-benders with portraits of theorists ! The result is a readable crash course in randomness.' New York Times 'If you're strong enough to have some of your favorite assumptions challenged, please read the Drunkard's Walk, a history, explanation, and exaltation of probability theory.' Fortune magazine

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Book SynopsisAn essential guide to the ways data can improve decision making. Statistics are everywhere: in news reports, at the doctor's office, and in every sort of forecast, from the stock market to the weather. Blogger, teacher, and computer scientist Allen B. Downey knows well that people have an innate ability both to understand statistics and to be fooled by them. As he makes clear in this accessible introduction to statistical thinking, the stakes are big. Simple misunderstandings have led to incorrect medical prognoses, underestimated the likelihood of large earthquakes, hindered social justice efforts, and resulted in dubious policy decisions. There are right and wrong ways to look at numbers, and Downey will help you see which are which. Probably Overthinking It uses real data to delve into real examples with real consequences, drawing on cases from health campaigns, political movements, chess rankings, and more. He lays out common pitfallslike the base rate fallacy, length-biased sampling, and Simpson's paradoxand shines a light on what we learn when we interpret data correctly, and what goes wrong when we don't. Using data visualizations instead of equations, he builds understanding from the basics to help you recognize errors, whether in your own thinking or in media reports. Even if you have never studied statisticsor if you have and forgot everything you learnedthis book will offer new insight into the methods and measurements that help us understand the world.Trade Review“Downey’s pure love for the subject shines through abundantly, as does his social conscience and belief in the importance of statistical methods to illuminate the greatest, most challenging issues of our time.” -- Aubrey Clayton, author of Bernoulli’s Fallacy: Statistical Illogic and the Crisis of Modern Science“Probably Overthinking It shows how fascinating and interesting statistics can be. Readers don’t need to be expert mathematicians. They just need to bring their curiosity about the world.” -- Ravin Kumar, data scientist at Google“Probably Overthinking It is a delightful exposition of commonly-encountered statistical fallacies and paradoxes and why they matter. The illustrations are powerful and the prose is exceptionally clear. There are few domains of human activity to which the lessons of this volume are not applicable.” -- Samuel H. Preston, coauthor of Demography: Measuring and Modeling Population Processes“Mark Twain once observed that ‘facts are stubborn things, but statistics are more pliable.’ Downey understands just how that happens, even to people who are not trying to obfuscate. It was an honest researcher who in 1971 found data that seemed to indicate smoking by pregnant women might be good for their babies—a misinterpretation that may have delayed anti-smoking measures by a decade. In this clear and cogent analysis, Downey explains why the data was misunderstood, as well as much else. It is a valuable book.” -- Floyd Norris, Johns Hopkins University, former chief financial correspondent for the New York TimesTable of ContentsIntroduction 1. Are You Normal? Hint: No 2. Relay Races and Revolving Doors 3. Defy Tradition, Save the World 4. Extremes, Outliers, and GOATs 5. Better Than New 6. Jumping to Conclusions 7. Causation, Collision, and Confusion 8. The Long Tail of Disaster 9. Fairness and Fallacy 10. Penguins, Pessimists, and Paradoxes 11. Changing Hearts and Minds 12. Chasing the Overton Window Epilogue Acknowledgments Bibliography Index

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Book SynopsisR is rapidly becoming the standard software for statistical analyses, graphical presentation of data, and programming in the natural, physical, social, and engineering sciences. Getting Started with R is now the go-to introductory guide for biologists wanting to learn how to use R in their research. It teaches readers how to import, explore, graph, and analyse data, while keeping them focused on their ultimate goals: clearly communicating their data in oral presentations, posters, papers, and reports. It provides a consistent workflow for using R that is simple, efficient, reliable, and reproducible.This second edition has been updated and expanded while retaining the concise and engaging nature of its predecessor, offering an accessible and fun introduction to the packages dplyr and ggplot2 for data manipulation and graphing. It expands the set of basic statistics considered in the first edition to include new examples of a simple regression, a one-way and a two-way ANOVA. Finally, it introduces a new chapter on the generalised linear model.Getting Started with R is suitable for undergraduates, graduate students, professional researchers, and practitioners in the biological sciences.Trade ReviewReview from previous edition The book would make the ideal text for a short course on data management and presentation - it truly packs an amazing amount of wisdom and wit between slim covers. * Trends in Ecology and Evolution *I was engaged by the refreshing style of the authors, that while informal, gives the user clear step-by-step instructions for using the software. Apart from the clear biological leaning of the example data, this book is applicable to anyone learning R (even a statistician!). * Significance *Table of ContentsPreface 1: Getting and getting acquainted with R 2: Getting your data into R 3: Data management, manipulation, and exploration with dplyr 4: Visualising your data 5: Introducing statistics in R 6: Advancing your statistics in R 7: Getting started with generalised linear models 8: Pimping your plots: scales and themes in ggplot2 9: Closing remarks Appendices

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Book SynopsisA refreshing, student-focused introduction to the use of statistics in the study of the biosciences. Emphasising why statistical techniques are essential tools for bioscientists, Biomeasurement removes the stigma attached to statistics by giving students the confidence to use key techniques for themselves.Trade ReviewReview from previous edition Biomeasurement does a wonderful job of keeping the biology the focus of analysis, and highlighting the fact that statistics is simply another useful tool to help biological understanding. * Dr Shane Richards, Biological and Biomedical Sciences, University of Durham, UK *This book represents the best I have seen for teaching undergraduate biologists statistics. * Dr Chris Venditti, Department of Biological Sciences, University of Hull, UK *It demystifies and clarifies topics that students can normally find confusing and challenging. It is a must for biologists! * Dr Maria G. Tuohy, School of Natural Sciences, National University of Ireland, Galway *This book was a blessing when I got it for my first year, and I'm still finding it helpful in my second year! It is so easy to navigate; you can read it cover to cover if you are very confused, or just dip into the topics you need. I would definitely recommend it to any students doing a bioscience degree which involves statistical elements. * Bethany Richmond, student at the University of Warwick *As a student with limited mathematical ability, new to statistics who believed I would not be able to pass this module, I read this book chapter by chapter prior to my weekly lectures and everything fell into place without a struggle. A 100% necessary purchase. A 100% necessary read. The book is appealing and very easy to navigate. I have tried to read other statistics books aimed at beginners but this was the only book which I clearly understood. * Julie Carter, student at Anglia Ruskin University *Table of Contents1: Why am I reading this book?2: Getting to grips with the basics3: Describing a single sample4: Inferring and estimating5: Choosing the right test and graph6: Overview of null hypothesis significance testing7: Tests on frequencies8: Tests of difference: two unrelated samples9: Tests of difference: two related samples10: Tests of difference: more than two samples11: Tests of relationship: regression12: Tests of relationship: correlation13: Introducing the generalized linear model: general linear model14: More on the generalized linear model: logistic and loglinear modelsAppendix I How to enter data into SPSSAppendix II Statistical tables of critical valuesAppendix III Summary guidance on reporting statistical resultsAppendix IV Statistics and experimental designRelated Titles

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Book SynopsisThe book provides insights in the decision-making for implementing strategies in various spheres of real-world issues. It integrates optimal policies in various decision­making problems and serves as a reference for researchers and industrial practitioners. Furthermore, the book provides sound knowledge of modelling of real-world problems and solution procedure using the various optimisation and statistical techniques for making optimal decisions. The book is meant for teachers, students, researchers and industrialists who are working in the field of materials science, especially operations research and applied statistics. Table of Contents1. A New Version of the Generalized Rayleigh Distribution with Copula, Properties, Applications and Different Methods of Estimation 2. Expanding the Burr X Model: Properties, Copula, Real Data Modeling and Different Methods of Estimation 3. Transmuted Burr Type X Model with Applications to Life Time Data 4. Monitoring Patients Blood Level through Enhanced Control Chart 5. Goodness of Fit in Parametric and Non-parametric Econometric Models 6. Stochastic Models for Cancer Progression and its Optimal Programming for Control with Chemotherapy 7. A New Unrelated Question Model with Two Questions Per Card 8. Hybrid of Simple Model and a New Unrelated Question Model for Two Sensitive Characteristics 9. Hybrid of Crossed Model and a New Unrelated Question Model for Two Sensitive Characteristics 10. Modified Regression Type Estimator by Ingeniously Utilizing Probabilities for more Efficient Results in Randomized Response Sampling 11. Ratio and Regression Type Estimators for a New Measure of Coefficient of Dispersion Relative to the Empirical Mode 12. Class of Exponential Ratio Type Estimator for Population Mean in Adaptive Cluster Sampling 13. An Inventory Model for Substitutable Deteriorating Products under Fuzzy and Cloud Fuzzy Demand Rate 14. Co-ordinated Selling Price and Replenishment Policies for Duopoly Retailers under Quadratic Demand and Deteriorating Nature of Items15. Quadratic Programming Approach for the Optimal Multi-objective Transportation Problem 16. Analyzing Multi-Objective Fixed-Charge Solid Transportation Problem under Rough and Fuzzy-Rough Environments 17. Overall Shale Gas Water Management: A Neutrosophic Optimization Approach 18. Memory Effect on an EOQ Model with Price Dependant Demand and Deterioration 19. Optimality Conditions of an Unconstrained Imprecise Optimization Problem via Interval Order Relation 20. Power Comparison of Different Goodness of Fit Tests for Beta Generalized Weibull Distribution 21. On the Transmuted Modified Lindley Distribution: Theory and Applications to Lifetime Data 22. Adjusted Bias and Risk for Estimating Treatment Effect after Selection with an Application in Idiopathic Osteoporosis 23. Validity Judgement of an EOQ Model using Phi-coefficient 24. Uncertain Chance-Constrained Multi-Objective Geometric Programming Problem 25. Optimal Decision Making for the Prediction of Diabetic Retinopathy in Type 2 Diabetes Mellitus Patients

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Book SynopsisThis book is intended to serve as a bridge in statistics for graduates and business practitioners interested in using their skills in the area of data science and analytics as well as statistical analysis in general. On the one hand, the book is intended to be a refresher for readers who have taken some courses in statistics, but who have not necessarily used it in their day-to-day work. On the other hand, the material can be suitable for readers interested in the subject as a first encounter with statistical work in Python. Statistics and Data Visualisation with Python aims to build statistical knowledge from the ground up by enabling the reader to understand the ideas behind inferential statistics and begin to formulate hypotheses that form the foundations for the applications and algorithms in statistical analysis, business analytics, machine learning, and applied machine learning. This book begins with the basics of programming in Python and data analysTable of Contents1. Data, Stats and Stories - An Introduction 2. Python Programming Primer 3. Snakes, Bears & Other Numerical Beasts: NumPy, SciPy & Pandas 4. The Measure of All Things - Statistics 5. Definitely Maybe: Probability and Distributions 6. Alluring Arguments and Ugly Facts - Statistical Modelling and Hypothesis Testing 7. Delightful Details - Data Visualisation 8. Dazzling Data Designs - Creating Charts A. Variance: Population v Sample B. Sum of First n Integers C. Sum of Squares of the First n Integers D. The Binomial Coefficient E. The Hypergeometric Distribution F. The Poisson Distribution G. The Normal Distribution H. Skewness and Kurtosis I. Kruskal-Wallis Test - No Ties

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Book SynopsisBased on the syllabus of the actuarial profession courses on general insurance pricing â with additional material inspired by the authorâs own experience as a practitioner and lecturer â Pricing in General Insurance, Second Edition presents pricing as a formalised process that starts with collecting information about a particular policyholder or risk and ends with a commercially informed rate. The first edition of the book proved very popular among students and practitioners with its pragmatic approach, informal style, and wide-ranging selection of topics, including: Background and context for pricing Process of experience rating, ranging from traditional approaches (burning cost analysis) to more modern approaches (stochastic modelling) Exposure rating for both property and casualty products Specialised techniques for personal lines (e.g., GLMs), reinsurance, and specific products such as credit risk and weatheTable of Contents1.The Pricing Process: A Gentle Start. 2. Insurance and Reinsurance Products. 3.The Cover Structure.4. The Insurance Markets. 5. Pricing in Context. 6. The Scientific Basis for Pricing: Risk Theory. 7. Familiarise Yourself with the Risk. 8. Data Requirements for Pricing. 9. Setting the Loss Inflation Assumptions. 10. Data Preparation. 11. The Burning Cost Approach. 12. What Is This Thing Called Modelling? A Gentle Introduction to Machine Learning. 13. Frequency Modelling: Adjusting for Claim Count IBNR. 14. Frequency Modelling: Selecting and Calibrating a Frequency Model. 15. Severity Modelling: Adjusting for IBNER and Other Factors. 16. Severity Modelling: Selecting and Calibrating a Severity Model. 17. Aggregate Loss Modelling. 18. Identifying, Measuring, and Communicating Uncertanity. 19. Setting the Premium. 20. The Pricing Cycle and Rate Change Calculations. 21. Experience Rating for Non-Proportional Reinsurance. 22. Exposure Rating for Property Insurance. 23. Liability Rating Using Increased Limit Factor Curves. 24. Pricing Considerations for Specific Lines of Business. 25. Catastrophe Modelling in Pricing. 26. Credibilty Theory. 27. Rating Factor Selection and Calibration: GLMs, GAMs, and Regularisation. 28. Multilevel Factors and Smoothing. 29. Pricing Multiple Lines of Business and Risks. 30. Insurance Structure Optimisation. 31. An Introduction to Pricing Models.

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Book Synopsis* Montgomery, Runger, and Hubele provide modern coverage of engineering statistics, focusing on how statistical tools are integrated into the engineering problem-solving process.Table of ContentsChapter 1 The Role of Statistics in Engineering 1 1-1 The Engineering Method and Statistical Thinking 2 1-2 Collecting Engineering Data 6 1-2.1 Retrospective Study 7 1-2.2 Observational Study 8 1-2.3 Designed Experiments 9 1-2.4 Random Samples 12 1-3 Mechanistic and Empirical Models 15 1-4 Observing Processes Over Time 17 Chapter 2 Data Summary and Presentation 23 2-1 Data Summary and Display 24 2-2 Stem-and-Leaf Diagram 29 2-3 Histograms 34 2-4 Box Plot 39 2-5 Time Series Plots 41 2-6 Multivariate Data 46 Chapter 3 Random Variables and Probability Distributions 57 3-1 Introduction 58 3-2 Random Variables 60 3-3 Probability 62 3-4 Continuous Random Variables 66 3-4.1 Probability Density Function 66 3-4.2 Cumulative Distribution Function 68 3-4.3 Mean and Variance 70 3-5 Important Continuous Distributions 74 3-5.1 Normal Distribution 74 3-5.2 Lognormal Distribution 84 3-5.3 Gamma Distribution 86 3-5.4 Weibull Distribution 86 3-5.5 Beta Distribution 88 3-6 Probability Plots 92 3-6.1 Normal Probability Plots 92 3-6.2 Other Probability Plots 94 3-7 Discrete Random Variables 97 3-7.1 Probability Mass Function 97 3-7.2 Cumulative Distribution Function 98 3-7.3 Mean and Variance 99 3-8 Binomial Distribution 102 3-9 Poisson Process 109 3-9.1 Poisson Distribution 109 3-9.2 Exponential Distribution 113 3-10 Normal Approximation to the Binomial and Poisson Distributions 119 3-11 More than One Random Variable and Independence 123 3-11.1 Joint Distributions 123 3-11.2 Independence 124 3-12 Functions of Random Variables 129 3-12.1 Linear Functions of Independent Random Variables 130 3-12.2 Linear Functions of Random Variables That are Not Independent 131 3-12.3 Nonlinear Functions of Independent Random Variables 133 3-13 Random Samples, Statistics, and the Central Limit Theorem 136 Chapter 4 Decision Making for a Single Sample 148 4-1 Statistical Inference 149 4-2 Point Estimation 150 4-3 Hypothesis Testing 156 4-3.1 Statistical Hypotheses 156 4-3.2 Testing Statistical Hypotheses 158 4-3.3 P-Values in Hypothesis Testing 164 4-3.4 One-Sided and Two-Sided Hypotheses 166 4-3.5 General Procedure for Hypothesis Testing 167 4-4 Inference on the Mean of a Population, Variance Known 169 4-4.1 Hypothesis Testing on the Mean 169 4-4.2 Type II Error and Choice of Sample Size 173 4-4.3 Large-Sample Test 177 4-4.4 Some Practical Comments on Hypothesis Testing 177 4-4.5 Confidence Interval on the Mean 178 4-4.6 General Method for Deriving a Confidence Interval 184 4-5 Inference on the Mean of a Population, Variance Unknown 186 4-5.1 Hypothesis Testing on the Mean 187 4-5.2 Type II Error and Choice of Sample Size 193 4-5.3 Confidence Interval on the Mean 195 4-6 Inference on the Variance of a Normal Population 199 4-6.1 Hypothesis Testing on the Variance of a Normal Population 199 4-6.2 Confidence Interval on the Variance of a Normal Population 203 4-7 Inference on a Population Proportion 205 4-7.1 Hypothesis Testing on a Binomial Proportion 205 4-7.2 Type II Error and Choice of Sample Size 208 4-7.3 Confidence Interval on a Binomial Proportion 210 4-8 Other Interval Estimates for a Single Sample 216 4-8.1 Prediction Interval 216 4-8.2 Tolerance Intervals for a Normal Distribution 217 4-9 Summary Tables of Inference Procedures for a Single Sample 219 4-10 Testing for Goodness of Fit 219 Chapter 5 Decision Making for Two Samples 230 5-1 Introduction 231 5-2 Inference on the Means of Two Populations, Variances Known 232 5-2.1 Hypothesis Testing on the Difference in Means, Variances Known 233 5-2.2 Type II Error and Choice of Sample Size 234 5-2.3 Confidence Interval on the Difference in Means, Variances Known 235 5-3 Inference on the Means of Two Populations, Variances Unknown 239 5-3.1 Hypothesis Testing on the Difference in Means 239 5-3.2 Type II Error and Choice of Sample Size 246 5-3.3 Confidence Interval on the Difference in Means 247 5-4 The Paired t-Test 252 5-5 Inference on the Ratio of Variances of Two Normal Populations 259 5-5.1 Hypothesis Testing on the Ratio of Two Variances 259 5-5.2 Confidence Interval on the Ratio of Two Variances 263 5-6 Inference on Two Population Proportions 265 5-6.1 Hypothesis Testing on the Equality of Two Binomial Proportions 265 5-6.2 Type II Error and Choice of Sample Size 268 5-6.3 Confidence Interval on the Difference in Binomial Proportions 269 5-7 Summary Tables for Inference Procedures for Two Samples 271 5-8 What if We Have More than Two Samples? 272 5-8.1 Completely Randomized Experiment and Analysis of Variance 272 5-8.2 Randomized Complete Block Experiment 281 Chapter 6 Building Empirical Models 298 6-1 Introduction to Empirical Models 299 6-2 Simple Linear Regression 304 6-2.1 Least Squares Estimation 304 6-2.2 Testing Hypotheses in Simple Linear Regression 312 6-2.3 Confidence Intervals in Simple Linear Regression 315 6-2.4 Prediction of a Future Observation 318 6-2.5 Checking Model Adequacy 319 6-2.6 Correlation and Regression 322 6-3 Multiple Regression 326 6-3.1 Estimation of Parameters in Multiple Regression 326 6-3.2 Inferences in Multiple Regression 331 6-3.3 Checking Model Adequacy 336 6-4 Other Aspects of Regression 344 6-4.1 Polynomial Models 344 6-4.2 Categorical Regressors 346 6-4.3 Variable Selection Techniques 348 Chapter 7 Design of Engineering Experiments 360 7-1 The Strategy of Experimentation 361 7-2 Factorial Experiments 362 7-3 2k Factorial Design 365 7-3.1 22 Design 366 7-3.2 Statistical Analysis 368 7-3.3 Residual Analysis and Model Checking 374 7-3.4 2k Design for k ≥ 3 Factors 376 7-3.5 Single Replicate of a 2k Design 382 7-4 Center Points and Blocking in 2k Designs 390 7-4.1 Addition of Center Points 390 7-4.2 Blocking and Confounding 393 7-5 Fractional Replication of a 2k Design 398 7-5.1 One-Half Fraction of a 2k Design 398 7-5.2 Smaller Fractions: 2k-pFractional Factorial Designs 404 7-6 Response Surface Methods and Designs 414 7-6.1 Method of Steepest Ascent 416 7-6.2 Analysis of a Second-Order Response Surface 418 7-7 Factorial Experiments With More Than Two Levels 424 Chapter 8 Statistical Process Control 438 8-1 Quality Improvement and Statistical Process Control 439 8-2 Introduction to Control Charts 440 8-2.1 Basic Principles 440 8-2.2 Design of a Control Chart 444 8-2.3 Rational Subgroups 446 8-2.4 Analysis of Patterns on Control Charts 447 8-3 X̄ and R Control Charts 449 8-4 Control Charts For Individual Measurements 456 8-5 Process Capability 461 8-6 Attribute Control Charts 465 8-6.1 P Chart (Control Chart for Proportions) and nP Chart 465 8-6.2 U Chart (Control Chart for Average Number of Defects per Unit) and C Chart 467 8-7 Control Chart Performance 470 8-8 Measurement Systems Capability 473 Appendices 483 Appendix A Statistical Tables and Charts 485 Appendix B Bibliography 500 Appendix C* Answers to Selected Exercises 502 Index 511

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Book Synopsis

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Book SynopsisIntroduction to Stochastic Finance with Market Examples, Second Edition presents an introduction to pricing and hedging in discrete and continuous-time financial models, emphasizing both analytical and probabilistic methods. It demonstrates both the power and limitations of mathematical models in finance, covering the basics of stochastic calculus for finance, and details the techniques required to model the time evolution of risky assets. The book discusses a wide range of classical topics including BlackScholes pricing, American options, derivatives, term structure modeling, and change of numéraire. It also builds up to special topics, such as exotic options, stochastic volatility, and jump processes.New to this Edition New chapters on Barrier Options, Lookback Options, Asian Options, Optimal Stopping Theorem, and Stochastic Volatility Contains over 235 exercises and 16 problems with complete solutions available online from the iTable of ContentsIntroduction. 1. Assets, Portfolios, and Arbitrage. 1.1. Portfolio Allocation and Short Selling. 1.2. Arbitrage. 1.3. Risk-Neutral Probability Measures. 1.4. Hedging of Contingent Claims. 1.5. Market Completeness. 1.6. Example: Binary Market. Exercises. 2. Discrete-Time Market Model. 2.1. Discrete-Time Compounding. 2.2. Arbitrage and Self-Financing Portfolios. 2.3. Contingent Claims. 2.4. Martingales and Conditional Expectations. 2.5. Market Completeness and Risk-Neutral Measures. 2.6. The Cox-Ross-Rubinstein (CRR) Market Model. Exercises. 3. Pricing and Hedging in Discrete Time. 3.1. Pricing Contingent Claims. 3.2. Pricing Vanilla Options in the CRR Model. 3.3. Hedging Contingent Claims. 3.4. Hedging Vanilla Options. 3.5. Hedging Exotic Options. 3.6. Convergence of the CRR Model. Exercises. 4. Brownian Motion and Stochastic Calculus. 4.1. Brownian Motion. 4.2. Three Constructions of Brownian Motion. 4.3. Wiener Stochastic Integral. 4.4. Itô Stochastic Integral. 4.5. Stochastic Calculus. Exercises. 5. Continuous-Time Market Model. 5.1. Asset Price Modeling. 5.2. Arbitrage and Risk-Neutral Measures. 5.3. Self-Financing Portfolio Strategies. 5.4. Two-Asset Portfolio Model. 5.5. Geometric Brownian Motion. Exercises. 6. Black-Scholes Pricing and Hedging. 6.1. The Black-Scholes PDE. 6.2. European Call Options. 6.3. European Put Options. 6.4. Market Terms and Data. 6.5. The Heat Equation. 6.6. Solution of the Black-Scholes PDE. Exercises. 7. Martingale Approach to Pricing and Hedging. 7.1. Martingale Property of the Itô Integral. 7.2. Risk-neutral Probability Measures. 7.3. Change of Measure and the Girsanov Theorem. 7.4. Pricing by the Martingale Method. 7.5. Hedging by the Martingale Method. Exercises. 8. Stochastic Volatility. 8.1. Stochastic Volatility Models. 8.2. Realized Variance Swaps. 8.3. Realized Variance Options. 8.4. European Options - PDE Method. 8.5. Perturbation Analysis. Exercises. 9. Volatility Estimation. 9.1. Historical Volatility. 9.2. Implied Volatility. 9.3. Local Volatility. 9.4. The VIX® Index. Exercises. 10. Maximum of Brownian motion. 10.1. Running Maximum of Brownian Motion. 10.2. The Reflection Principle. 10.3. Density of the Maximum of Brownian Motion. 10.4. Average of Geometric Brownian Extrema. Exercises. 11. Barrier Options. 11.1. Options on Extrema. 11.2. Knock-Out Barrier. 11.3. Knock-In Barrier. 11.4. PDE Method. 11.5. Hedging Barrier Options. Exercises. 12. Lookback Options. 12.1. The Lookback Put Option. 12.2. PDE Method. 12.3. The Lookback Call Option. 12.4. Delta Hedging for Lookback Options. Exercises. 13. Asian Options. 13.1. Bounds on Asian Option Prices. 13.2. Hartman-Watson Distribution. 13.3. Laplace Transform Method. 13.4. Moment Matching Approximations. 13.5. PDE Method. Exercises. 14. Optimal Stopping Theorem. 14.1. Filtrations and Information Flow. 14.2. Submartingales and Supermartingales. 14.3. Optimal Stopping Theorem. 14.4. Drifted Brownian Motion. Exercises. 15. American Options. 15.1. Perpetual American Put Options. 15.2. PDE Method for Perpetual Put Options. 15.3. Perpetual American Call Options. 15.4. Finite Expiration American Options. 15.5. PDE Method with Finite Expiration. Exercises. 16. Change of Numéraire and Forward Measures. 16.1. Notion of Numéraire. 16.2. Change of Numéraire. 16.3. Foreign Exchange. 16.4. Pricing Exchange Options. 16.5. Hedging by Change of Numéraire. Exercises. 17. Short Rates and Bond Pricing. 17.1. Vasicek model. 17.2. Affine Short Rate Models. 17.3. Zero-Coupon and Coupon Bonds. 17.4. Bond Pricing PDE. Exercises. 18. Forward Rates. 18.1. Construction of Forward Rates. 18.2. LIBOR/SOFR Swap Rates. 18.3. The HJM Model. 18.4. Yield Curve Modeling. 18.5. Two-Factor Model. 18.6. The BGM Model. Exercises. 19. Pricing of Interest Rate Derivatives. 19.1. Forward Measures and Tenor Structure. 19.2. Bond Options. 19.3. Caplet Pricing. 19.4. Forward Swap Measures. 19.5. Swaption Pricing. Exercises. 20. Stochastic Calculus for Jump Processes. 20.1. The Poisson Process. 20.2. Compound Poisson Process. 20.3. Stochastic Integrals and Itô Formula with Jumps. 20.4. Stochastic Differential Equations with Jumps. 20.5. Girsanov Theorem for Jump Processes. Exercises. 21. Pricing and Hedging in Jump Models. 21.1. Fitting the Distribution of Market Returns. 21.2. Risk-Neutral Probability Measures. 21.3. Pricing in Jump Models. 21.4. Exponential Lévy Models. 21.5. Black-Scholes PDE with Jumps. 21.6. Mean-Variance Hedging with Jumps. Exercises. 22. Basic Numerical Methods. 22.1. Discretized Heat Equation. 22.2. Discretized Black-Scholes PDE. 22.3. Euler Discretization. 22.4. Milshtein Discretization. Exercises. Bibliography. Index

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