Mendelian Randomization: Methods For Causal Inference Using Genetic Variants provides thorough coverage of the methods and practical elements of Mendelian randomization analysis. It brings together diverse aspects of Mendelian randomization from the fields of epidemiology, statistics, genetics, and bioinformatics. Through multiple examples, the first part of the book introduces the reader to the concept of Mendelian randomization, showing how to perform simple Mendelian randomization investigations and interpret the results. The second part of the book addresses specific methodological issues relevant to the practice of Mendelian randomization, including robust methods, weak instruments, multivariable methods, and power calculations. The authors present the theoretical aspects of these issues in an easy-to-understand way by using non-technical language. The last part of the book examines the potential for Mendelian randomization in the future, exploring both methodological and applied developments. Features Offers first-hand, in-depth guidance on Mendelian randomization from leaders in the field Makes the diverse aspects of Mendelian randomization understandable to newcomers Illustrates technical details using data from applied analyses Discusses possible future directions for research involving Mendelian randomization Software code is provided in the relevant chapters and is also available at the supplementary website This book gives epidemiologists, statisticians, geneticists, and bioinformaticians the foundation to understand how to use genetic variants as instrumental variables in observational data. New in Second Edition: The second edition of the book has been substantially re-written to reduce the amount of technical content, and emphasize practical consequences of theoretical issues. Extensive material on the use of two-sample Mendelian randomization and publicly-available summarized data has been added. The book now includes several real-world examples that show how Mendelian randomization can be used to address questions of disease aetiology, target validation, and drug development

In recent years, the study of difference equations has acquired a new significance, due in large part to their use in the formulation and analysis of discrete-time systems, the numerical integration of differential equations by finite-difference schemes, and the study of deterministic chaos. The second edition of Difference Equations: Theory and Applications provides a thorough listing of all major theorems along with proofs. The text treats the case of first-order difference equations in detail, using both analytical and geometrical methods. Both ordinary and partial difference equations are considered, along with a variety of special nonlinear forms for which exact solutions can be determined. Numerous worked examples and problems allow readers to fully understand the material in the text. They also give possible generalization of the theorems and application models. The text's expanded coverage of application helps readers appreciate the benefits of using difference equations in the modeling and analysis of "realistic" problems from a broad range of fields. The second edition presents, analyzes, and discusses a large number of applications from the mathematical, biological, physical, and social sciences. Discussions on perturbation methods and difference equation models of differential equation models of differential equations represent contributions by the author to the research literature. Reference to original literature show how the elementary models of the book can be extended to more realistic situations. Difference Equations, Second Edition gives readers a background in discrete mathematics that many workers in science-oriented industries need as part of their general scientific knowledge. With its minimal mathematical background requirements of general algebra and calculus, this unique volume will be used extensively by students and professional in science and technology, in areas such as applied mathematics, control theory, population science, economics, and electronic circuits, especially discrete signal processing.

This Sixth Edition of Calculus continues the effort to promote courses in which understanding and computation reinforce each other. Calculus: Multivariable 6th Edition reflects the many voices of users at research universities, four-year colleges, community colleges, and secondary schools. This new edition has been streamlined to create a flexible approach to both theory and modeling. For instructors wishing to emphasize the connection between calculus and other fields, the text includes a variety of problems and examples from the physical, health, and biological sciences, engineering and economics. In addition, new problems on the mathematics of sustainability and new case studies on calculus in medicine by David E. Sloane, MD have been added.

This text introduces engineering students to probability theory and stochastic processes. Along with thorough mathematical development of the subject, the book presents intuitive explanations of key points in order to give students the insights they need to apply math to practical engineering problems. The first seven chapters contain the core material that is essential to any introductory course. In one-semester undergraduate courses, instructors can select material from the remaining chapters to meet their individual goals. Graduate courses can cover all chapters in one semester.

This official Student Solutions Manual includes solutions to the odd-numbered exercises featured in the second edition of Steven Strogatz's classic text Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering. The textbook and accompanying Student Solutions Manual are aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. Complete with graphs and worked-out solutions, this manual demonstrates techniques for students to analyze differential equations, bifurcations, chaos, fractals, and other subjects Strogatz explores in his popular book.

Librarians understand the need to store, use and analyze data related to their collection, patrons and institution, and there has been consistent interest over the last 10 years to improve data management, analysis, and visualization skills within the profession. However, librarians find it difficult to move from out-of-the-box proprietary software applications to the skills necessary to perform the range of data science actions in code. This book will focus on teaching R through relevant examples and skills that librarians need in their day-to-day lives that includes visualizations but goes much further to include web scraping, working with maps, creating interactive reports, machine learning, and others. While there’s a place for theory, ethics, and statistical methods, librarians need a tool to help them acquire enough facility with R to utilize data science skills in their daily work, no matter what type of library they work at (academic, public or special). By walking through each skill and its application to library work before walking the reader through each line of code, this book will support librarians who want to apply data science in their daily work. Hands-On Data Science for Librarians is intended for librarians (and other information professionals) in any library type (public, academic or special) as well as graduate students in library and information science (LIS). Key Features: Only data science book available geared toward librarians that includes step-by-step code examples Examples include all library types (public, academic, special) Relevant datasets Accessible to non-technical professionals Focused on job skills and their applications

This book aims to increase the visibility of data science in real-world, which differs from what you learn from a typical textbook. Many aspects of day-to-day data science work are almost absent from conventional statistics, machine learning, and data science curriculum. Yet these activities account for a considerable share of the time and effort for data professionals in the industry. Based on industry experience, this book outlines real-world scenarios and discusses pitfalls that data science practitioners should avoid. It also covers the big data cloud platform and the art of data science, such as soft skills. The authors use R as the primary tool and provide code for both R and Python. This book is for readers who want to explore possible career paths and eventually become data scientists. This book comprehensively introduces various data science fields, soft and programming skills in data science projects, and potential career paths. Traditional data-related practitioners such as statisticians, business analysts, and data analysts will find this book helpful in expanding their skills for future data science careers. Undergraduate and graduate students from analytics-related areas will find this book beneficial to learn real-world data science applications. Non-mathematical readers will appreciate the reproducibility of the companion R and python codes. Key Features: * It covers both technical and soft skills. * It has a chapter dedicated to the big data cloud environment. For industry applications, the practice of data science is often in such an environment. * It is hands-on. We provide the data and repeatable R and Python code in notebooks. Readers can repeat the analysis in the book using the data and code provided. We also suggest that readers modify the notebook to perform analyses with their data and problems, if possible. The best way to learn data science is to do it!

The book is a follow-up to the first book on the topic published here. The book can be used for teaching and research purposes. The book offers different techniques for investigations of Ordinary and Partial Differential Equations and should promote interest in functional analysis.

Stochastic Differential Equations for Science and Engineering is aimed at students at the M.Sc. and PhD level. The book describes the mathematical construction of stochastic differential equations with a level of detail suitable to the audience, while also discussing applications to estimation, stability analysis, and control. The book includes numerous examples and challenging exercises. Computational aspects are central to the approach taken in the book, so the text is accompanied by a repository on GitHub containing a toolbox in R which implements algorithms described in the book, code that regenerates all figures, and solutions to exercises. Features: Contains numerous exercises, examples, and applications Suitable for science and engineering students at Master's or PhD level Thorough treatment of the mathematical theory combined with an accessible treatment of motivating examples GitHub repository available at: https://github.com/Uffe-H-Thygesen/SDEbook and https://github.com/Uffe-H-Thygesen/SDEtools

How many colors are needed to color a map? Must hailstones numbers always fall to the ground? Can statistics prove anything? What is a perfect square, and who has found the ultimate one? How do numbers affect national security? What kinds of problems confront the traveling salesman? Does anyone know how best to pack balls together? What is life like in 4 (or 3 1/2) dimensions? How does a clock count, and why should we care? What number secrets do sunflowers and pine cones conceal? What is a monster doing in mathematics? These and many other fascinating questions about familiar numbers like 1, 2, and 3 are explored in Malcolm Line's second adventure into the world of numbers. Written in a lively and readable style, Think of a Number relates the story of some of the most famous problems that have confronted the world's experts over the centuries, from the earliest interests of the ancient Greeks to the very cutting-edge of modern research involving today's most powerful computers. The book explores the relationship between numbers and nature in its broadest sense and discovers the beauty of fractals and chaos. Requiring little or no prior knowledge of mathematics, this resource will be fascinating reading for anyone with an interest in numbers and their role in the natural world.

Survival data analysis is a very broad field of statistics, encompassing a large variety of methods used in a wide range of applications, and in particular in medical research. During the last twenty years, several extensions of "classical" survival models have been developed to address particular situations often encountered in practice. This book aims to gather in a single reference the most commonly used extensions, such as frailty models (in case of unobserved heterogeneity or clustered data), cure models (when a fraction of the population will not experience the event of interest), competing risk models (in case of different types of event), and joint survival models for a time-to-event endpoint and a longitudinal outcome. Features Presents state-of-the art approaches for different advanced survival models including frailty models, cure models, competing risk models and joint models for a longitudinal and a survival outcome Uses consistent notation throughout the book for the different techniques presented Explains in which situation each of these models should be used, and how they are linked to specific research questions Focuses on the understanding of the models, their implementation, and their interpretation, with an appropriate level of methodological development for masters students and applied statisticians Provides references to existing R packages and SAS procedure or macros, and illustrates the use of the main ones on real datasets This book is primarily aimed at applied statisticians and graduate students of statistics and biostatistics. It can also serve as an introductory reference for methodological researchers interested in the main extensions of classical survival analysis.

From one of today's most accomplished and trusted mathematics authors comes a new textbook that offers unmatched support for students taking the AP (R) Calculus exam, and comes with additional resources for the teachers helping them prepare for it.Sullivan and Miranda's Calculus for the AP Course covers every Big Idea, Essential Knowledge statement, Learning Objective, and Math Practice described in the 2016-2017 redesigned College Board (TM) Curriculum Framework. It is concise and its focused narrative and integrated conceptual and problem-solving tools give students just the help they need as they learn calculus and prepare for the redesigned AP (R) Exam. Its accompanying Teacher's Edition provides an in depth correlation and abundant tips, examples, projects, and resources to ensure close adherence the new Curriculum Framework.

This book covers computational statistics-based approaches for Artificial Intelligence. The aim of this book is to provide comprehensive coverage of the fundamentals through the applications of the different kinds of mathematical modelling and statistical techniques and describing their applications in different Artificial Intelligence systems. The primary users of this book will include researchers, academicians, postgraduate students, and specialists in the areas of data science, mathematical modelling, and Artificial Intelligence. It will also serve as a valuable resource for many others in the fields of electrical, computer, and optical engineering. The key features of this book are: Presents development of several real-world problem applications and experimental research in the field of computational statistics and mathematical modelling for Artificial Intelligence Examines the evolution of fundamental research into industrialized research and the transformation of applied investigation into real-time applications Examines the applications involving analytical and statistical solutions, and provides foundational and advanced concepts for beginners and industry professionals Provides a dynamic perspective to the concept of computational statistics for analysis of data and applications in intelligent systems with an objective of ensuring sustainability issues for ease of different stakeholders in various fields Integrates recent methodologies and challenges by employing mathematical modeling and statistical techniques for Artificial Intelligence

Most of the real-life signals are non-stationary in nature. The examples of such signals include biomedical signals, communication signals, speech, earthquake signals, vibration signals, etc. Time-frequency analysis plays an important role for extracting the meaningful information from these signals. The book presents time-frequency analysis methods together with their various applications. The basic concepts of signals and different ways of representing signals have been provided. The various time-frequency analysis techniques namely, short-time Fourier transform, wavelet transform, quadratic time-frequency transforms, advanced wavelet transforms, and adaptive time-frequency transforms have been explained. The fundamentals related to these methods are included. The various examples have been included in the book to explain the presented concepts effectively. The recently developed time-frequency analysis techniques such as, Fourier-Bessel series expansion-based methods, synchrosqueezed wavelet transform, tunable-Q wavelet transform, iterative eigenvalue decomposition of Hankel matrix, variational mode decomposition, Fourier decomposition method, etc. have been explained in the book. The numerous applications of time-frequency analysis techniques in various research areas have been demonstrated. This book covers basic concepts of signals, time-frequency analysis, and various conventional and advanced time-frequency analysis methods along with their applications. The set of problems included in the book will be helpful to gain an expertise in time-frequency analysis. The material presented in this book will be useful for students, academicians, and researchers to understand the fundamentals and applications related to time-frequency analysis.

The burgeoning field of data science has provided a wealth of techniques for analysing large and complex geospatial datasets, including descriptive, explanatory, and predictive analytics. However, applying these methods is just one part of the overall process of geographic data science. Other critical steps include screening for suspect data values, handling missing data, harmonizing data from multiple sources, summarizing the data, and visualizing data and analysis results. Although there are many books available on statistical and machine learning methods, few encompass the broader topic of scientific workflows for geospatial data processing and analysis. The purpose of Geographic Data Science with R is to fill this gap by providing a series of tutorials aimed at teaching good practices for using geospatial data to address problems in environmental geography. It is based on the R language and environment, which currently provides the best option for working with diverse spatial and non-spatial data in a single platform. Fundamental techniques for processing and visualizing tabular, vector, and raster data are introduced through a series of practical examples followed by case studies that combine multiple types of data to address more complex problems. The book will have a broad audience. Both students and professionals can use it as a workbook to learn high-level techniques for geospatial data processing and analysis with R. It is also suitable as a textbook. Although not intended to provide a comprehensive introduction to R, it is designed to be accessible to readers who have at least some knowledge of coding but little to no experience with R. Key Features: Focus on developing practical workflows for processing and integrating multiple sources of geospatial data in R Example-based approach that teaches R programming and data science concepts through real-world applications related to climate, land cover and land use, and natural hazards. Consistent use of tidyverse packages for tabular data manipulation and visualization. Strong focus on analysing continuous and categorical raster datasets using the new terra package Organized so that each chapter builds on the topics and techniques covered in the preceding chapters Can be used for self-study or as the textbook for a geospatial science course.

This book covers statistical consequences of breaches of research integrity such as fabrication and falsification of data, and researcher glitches summarized as questionable research practices. It is unique in that it discusses how unwarranted data manipulation harms research results and that questionable research practices are often caused by researchers' inadequate mastery of the statistical methods and procedures they use for their data analysis. The author's solution to prevent problems concerning the trustworthiness of research results, no matter how they originated, is to publish data in publicly available repositories and encourage researchers not trained as statisticians not to overestimate their statistical skills and resort to professional support from statisticians or methodologists. The author discusses some of his experiences concerning mutual trust, fear of repercussions, and the bystander effect as conditions limiting revelation of colleagues' possible integrity breaches. He explains why people are unable to mimic real data and why data fabrication using statistical models stills falls short of credibility. Confirmatory and exploratory research and the usefulness of preregistration, and the counter-intuitive nature of statistics are discussed. The author questions the usefulness of statistical advice concerning frequentist hypothesis testing, Bayes-factor use, alternative statistics education, and reduction of situational disturbances like performance pressure, as stand-alone means to reduce questionable research practices when researchers lack experience with statistics.

Mathematics Applications and Interpretation for the IB Diploma Higher Level provides comprehensive coverage of the new curriculum, developed for first examinations in 2021. Written by a highly experienced IB author team, this book includes the following features: integrated GeoGebra applets created specifically for the course, worked examples to help you tackle questions and apply concepts and skills, practice questions to help you prepare for the exam, a rich and wide-ranging Theory of Knowledge chapter, and guidance on the Internal Assessment.

Structural equation modeling (SEM) is a very general and flexible multivariate technique that allows relationships among variables to be examined. The roots of SEM are in the social sciences. In writing this textbook, the authors look to make SEM accessible to a wider audience of researchers across many disciplines, addressing issues unique to health and medicine. SEM is often used in practice to model and test hypothesized causal relationships among observed and latent (unobserved) variables, including in analysis across time and groups. It can be viewed as the merging of a conceptual model, path diagram, confirmatory factor analysis, and path analysis. In this textbook the authors also discuss techniques, such as mixture modeling, that expand the capacity of SEM using a combination of both continuous and categorical latent variables. Features: Basic, intermediate, and advanced SEM topics Detailed applications, particularly relevant for health and medical scientists Topics and examples that are pertinent to both new and experienced SEM researchers Substantive issues in health and medicine in the context of SEM Both methodological and applied examples Numerous figures and diagrams to illustrate the examples As SEM experts situated among clinicians and multidisciplinary researchers in medical settings, the authors provide a broad, current, on the ground understanding of the issues faced by clinical and health services researchers and decision scientists. This book gives health and medical researchers the tools to apply SEM approaches to study complex relationships between clinical measurements, individual and community-level characteristics, and patient-reported scales.

This remarkable text by John R. Taylor has been a non-stop best-selling international hit since it was first published forty years ago. However, the two-plus decades since the second edition was released have seen two dramatic developments; the huge rise in popularity of Bayesian statistics, and the continued increase in the power and availability of computers and calculators. In response to the former, Taylor has added a full chapter dedicated to Bayesian thinking, introducing conditional probabilities and Bayes’ theorem. The several examples presented in the new third edition are intentionally very simple, designed to give readers a clear understanding of what Bayesian statistics is all about as their first step on a journey to become practicing Bayesians. In response to the second development, Taylor has added a number of chapter-ending problems that will encourage readers to learn how to solve problems using computers. While many of these can be solved using programs such as Matlab or Mathematica, almost all of them are stated to apply to commonly available spreadsheet programs like Microsoft Excel. These programs provide a convenient way to record and process data and to calculate quantities like standard deviations, correlation coefficients, and normal distributions; they also have the wonderful ability – if students construct their own spreadsheets and avoid the temptation to use built-in functions – to teach the meaning of these concepts.

Easy-to-Use Reference and Software for Statistical Modeling and Testing Handbook of Statistical Distributions with Applications, Second Edition provides quick access to common and specialized probability distributions for modeling practical problems and performing statistical calculations. Along with many new examples and results, this edition includes both the author's StatCalc software and R codes to accurately and easily carry out computations. New to the Second Edition Major changes in binomial, Poisson, normal, gamma, Weibull, exponential, logistic, Laplace, and Pareto distributions Updated statistical tests and intervals based on recent publications in statistical journals Enhanced PC calculator StatCalc with electronic help manuals R functions for cases where StatCalc is not applicable, with the codes available online This highly praised handbook integrates popular probability distribution models, formulas, applications, and software to help you compute a variety of statistical intervals. It covers probability and percentiles, algorithms for random number generation, hypothesis tests, confidence intervals, tolerance intervals, prediction intervals, sample size determination, and much more.

Presents a comprehensive review of classic hypersonic flow from the Newtonian theory to blast wave analogue. Introduces nonequilibrium chemical kinetics to gas dynamics for hypersonic flows in the high-enthalpy state. Integrates quantum mechanics to high-enthalpy hypersonic flows including dissociation and ionization. Covers the complete heat transfer process with radiative energy transfer for thermal protection of earth reentry vehicle. Develops and verifies the interdisciplinary governing equations for understanding and analyzing realistic hypersonic flows.

● Materials tested over three years with several cohorts of students at different levels (UG and PGT), based on experiences teaching these materials to professional crime analysts, and developed by researchers with over 20 year experience teaching crime mapping. ● Very practical and embedded integration of criminological, spatial statistics, and cartographic concepts with the focus placed on lay understanding and development of intuition for ‘professional/applied research’ practice rather than in mathematical formulation and proof. ● Moves away from heavy US focus of competing alternatives. Datasets and examples used come from a variety of national contexts (including the US) which should broaden its appeal.

Basics of Ramsey Theory serves as a gentle introduction to Ramsey theory for students interested in becoming familiar with a dynamic segment of contemporary mathematics that combines ideas from number theory and combinatorics. The core of the of the book consists of discussions and proofs of the results now universally known as Ramsey's theorem, van der Waerden's theorem, Schur's theorem, Rado's theorem, the Hales-Jewett theorem, and the Happy End Problem of Erdos and Szekeres. The aim is to present these in a manner that will be challenging but enjoyable, and broadly accessible to anyone with a genuine interest in mathematics. Features Suitable for any undergraduate student who has successfully completed the standard calculus sequence of courses and a standard first (or second) year linear algebra course. Filled with visual proofs of fundamental theorems. Contains numerous exercises (with their solutions) accessible to undergraduate students. Serves as both a textbook or as a supplementary text in an elective course in combinatorics and aimed at a diverse group of students interested in mathematics.

Revealing the flaws in human decision making, this book explores how AI can be used to optimise decisions for improved business outcomes and efficiency, as well as looking ahead into the significant contributions Decision Intelligence (DI) can make to society and the ethical challenges it may raise. Offering an impressive framework of Decision Intelligence (DI), from the theories and concepts used to design autonomous intelligent agents to the technologies that power DI systems and the ways in which companies use decision-making building blocks to build DI solutions that enable businesses to democratise AI, this book provides a systematic approach to AI intelligence and human involvement. Replete with case studies on DI application, as well as wider discussions on the social implications of the technology, this book appeals to both students of AI and data solutions and businesses considering DI adoption.

Building on the pioneering work by the Nobel Memorial Laureate, John Nash, Professor Thomson has brought together a broad selection of seminal articles which analyse and discuss bargaining and the theory of cooperative games. Beginning with a distinguished collection of papers discussing the origins of game theory, this volume systematically explores its development as a tool to illuminate economic behaviour. It includes the work of highly accomplished academics whose discoveries over the years have shaped the direction of this subject. With his insightful introduction, the editor has ensured that this indispensable book is suitable for anyone with an interest in cooperative gaming.