Association Models in Epidemiology
Focuses on integrating epidemiologic principles with statistical modeling methods in such a way that the principles inform the choice of modeling strategy and covariate selection.
Gaussian Integrals and their Applications
Gaussian Integrals form an integral part of many subfields of applied mathematics and physics, especially in topics such as probability theory, statistics, statistical mechanics, quantum mechanics and so on. They are essential in computing quantities such as the statistical properties of normal random variables, solving partial differential equations involving diffusion processes, and gaining insight into the properties of particles. In Gaussian Integrals and their Applications, the author has condensed the material deemed essential for undergraduate and graduate students of physics and mathematics, such that for those who are very keen would know what to look for next if their appetite for knowledge remains unsatisfied by the time they finish reading this book. Features A concise and easily digestible treatment of the essentials of Gaussian Integrals Suitable for advanced undergraduates and graduate students in mathematics, physics, and statistics The only prerequisites are a strong understanding of multivariable calculus and linear algebra. Supplemented by numerous exercises (with fully worked solutions) at the end, which pertain to various levels of difficulty and are inspired by different fields in which Gaussian integrals are used.
Biosecurity
Biosecurity: A Systems Perspective provides an overview of biosecurity as a system of related components, actors and risks.
Explorations in Monte Carlo Methods
Monte Carlo Methods are among the most used, and useful, computational tools available today. They provide efficient and practical algorithms to solve a wide range of scientific and engineering problems in dozens of areas many of which are covered in this text. These include simulation, optimization, finance, statistical mechanics, birth and death processes, Bayesian inference, quadrature, gambling systems and more.This text is for students of engineering, science, economics and mathematics who want to learn about Monte Carlo methods but have only a passing acquaintance with probability theory. The probability needed to understand the material is developed within the text itself in a direct manner using Monte Carlo experiments for reinforcement. There is a prerequisite of at least one year of calculus and a semester of matrix algebra.Each new idea is carefully motivated by a realistic problem, thus leading to insights into probability theory via examples and numerical simulations. Programming exercises are integrated throughout the text as the primary vehicle for learning the material. All examples in the text are coded in Python as a representative language; the logic is sufficiently clear so as to be easily translated into any other language. Further, Python scripts for each worked example are freely accessible for each chapter. Along the way, most of the basic theory of probability is developed in order to illuminate the solutions to the questions posed. One of the strongest features of the book is the wealth of completely solved example problems. These provide the reader with a sourcebook to follow towards the solution of their own computational problems. Each chapter ends with a large collection of homework problems illustrating and directing the material. This book is suitable as a textbook for students of engineering, finance, and the sciences as well as mathematics. The problem-oriented approach makes it ideal for an applied course in basic probability as well as for a more specialized course in Monte Carlo Methods. Topics include probability distributions, probability calculations, sampling, counting combinatorial objects, Markov chains, random walks, simulated annealing, genetic algorithms, option pricing, gamblers ruin, statistical mechanics, random number generation, Bayesian Inference, Gibbs Sampling and Monte Carlo integration.
Puzzle and Proof
This book is a compilation of the problems and solutions for the first ten years of the Utah Math Olympiad. The problems are challenging but should be understandable at a high school level. The book will be a fantastic resource for anyone who enjoys mathematical and/or logic puzzles.
Bayesian Inference
This book provides a comprehensive coverage of the fundamentals of Bayesian inference from all important perspectives, namely theory, methods and computations. All theoretical results are presented as formal theorems, corollaries, lemmas etc., furnished with detailed proofs.
Puzzle and Proof
This book is a compilation of the problems and solutions for the first ten years of the Utah Math Olympiad. The problems are challenging but should be understandable at a high school level. The book will be a fantastic resource for anyone who enjoys mathematical and/or logic puzzles.
Quantum Leaps
How does Google know what you want to type? How did humans first reach the moon? Could we ever have a supercomputer the size of a pinhead? In this thrilling numerical journey, Hugh Barker explores how mathematics has helped to build the technology of today, and the fascinating ways it is shaping the future. From green energy to 3-D printing and from quantum cryptography to machine learning, High Tech Maths reveals the hidden mathematics in modern technology. Beautifully written and full of ingenious examples, this book will make you realise how the modern world be impossible without our formidable mathematical armoury.
High-Dimensional Optimization
This book is interdisciplinary and unites several areas of applied probability, statistics, and computational mathematics including computer experiments, optimal experimental design, and global optimization. The bulk of the book is based on several recent papers by the authors but also contains new results. Considering applications, this brief highlights multistart and other methods of global optimizations requiring efficient exploration of the domain of optimization. This book is accessible to a wide range of readers; the prerequisites for reading the book are rather low, and many numerical examples are provided that pictorially illustrate the main ideas, methods, and conclusions. The main purpose of this book is the construction of efficient exploration strategies of high-dimensional sets. In high dimensions, the asymptotic arguments could be practically misleading and hence the emphasis on the non-asymptotic regime. An important link with global optimization stems from the observation that approximate covering is one of the key concepts associated with multistart and other key random search algorithms. In addition to global optimization, important applications of the results are computer experiments and machine learning. It is demonstrated that the asymptotically optimal space-filling designs, such as pure random sampling or low-discrepancy point nets, could be rather inefficient in the non-asymptotic regime and the authors suggest ways of increasing the efficiency of such designs. The range of techniques ranges from experimental design, Monte Carlo, and asymptotic expansions in the central limit theorem to multivariate geometry, theory of lattices, and numerical integration. This book could be useful to a wide circle of readers, especially those specializing in global optimization, numerical analysis, computer experiments, and computational mathematics. As specific recipes for improving set exploration schemes are formulated, the book can also be used by the practitioners interested in applications only.
Data Management in Large-Scale Education Research
This book is for those involved in a research study involving original data collection. Whilst it focuses on quantitative data, collected from human participants, many of the practices covered apply to other types of data. It contains foundational context, instructions, and examples.
Multivariate Analysis
Multivariate Analysis Comprehensive Reference Work on Multivariate Analysis and its Applications The first edition of this book, by Mardia, Kent and Bibby, has been used globally for over 40 years. This second edition brings many topics up to date, with a special emphasis on recent developments. A wide range of material in multivariate analysis is covered, including the classical themes of multivariate normal theory, multivariate regression, inference, multidimensional scaling, factor analysis, cluster analysis and principal component analysis. The book also now covers modern developments such as graphical models, robust estimation, statistical learning, and high-dimensional methods. The book expertly blends theory and application, providing numerous worked examples and exercises at the end of each chapter. The reader is assumed to have a basic knowledge of mathematical statistics at an undergraduate level together with an elementary understanding of linear algebra. There are appendices which provide a background in matrix algebra, a summary of univariate statistics, a collection of statistical tables and a discussion of computational aspects. The work includes coverage of: Basic properties of random vectors, copulas, normal distribution theory, and estimation Hypothesis testing, multivariate regression, and analysis of variance Principal component analysis, factor analysis, and canonical correlation analysis Discriminant analysis, cluster analysis, and multidimensional scaling New advances and techniques, including supervised and unsupervised statistical learning, graphical models and regularization methods for high-dimensional data Although primarily designed as a textbook for final year undergraduates and postgraduate students in mathematics and statistics, the book will also be of interest to research workers and applied scientists.
Mathematics of Tabletop Games
This book provides a bridge between mathematics and hobby tabletop gaming. Readers interested in either mathematics or tabletop games will find this book an engaging way to begin exploring the other topic or the connection between the topics.
From Data to Insights
This book offers a clear and accessible guide to cross-tabulation analysis, transforming a complex subject into an accessible topic. It diverges from traditional statistical texts, adopting a conversational tone that addresses common questions and concerns.
Analyzing Baseball Data with R
Analyzing Baseball Data with R Third Edition introduces R to sabermetricians, baseball enthusiasts, and students interested in exploring the richness of baseball data. It equips you with the necessary skills and software tools to perform all the analysis steps.
Mathematics of Tabletop Games
This book provides a bridge between mathematics and hobby tabletop gaming. Readers interested in either mathematics or tabletop games will find this book an engaging way to begin exploring the other topic or the connection between the topics.
Statistical Analyses for Criminal Justice and Criminology
This book is a how-to guide for statistical analyses designed for undergraduates and others new to the subject. It uses a conceptual framework, starting with the most basic concepts of statistics and moving up through the capacity to perform bivariate regression.
Bayesian Modeling of Spatio-Temporal Data with R
This book is designed to make spatio-temporal modeling and analysis understandable to students and researchers, mathematicians and statisticians and practitioners in the applied sciences. By avoiding hardcore math and calculus, this book aims to be a bridge that removes the statistical knowledge gap from among the applied scientists.
Parabolic Problems
Parabola is a mathematics magazine published by UNSW, Sydney. Among other things, each issue of Parabola has contained a collection of puzzles/problems, on various mathematical topics and at a suitable level for younger (but mathematically sophisticated) readers.Parabolic Problems: 60 Years of Mathematical Puzzles in Parabola collects the very best of almost 1800 problems and puzzles into a single volume. Many of the problems have been re-mastered, and new illustrations have been added. Topics covered range across geometry, number theory, combinatorics, logic, and algebra. Solutions are provided to all problems, and a chapter has been included detailing some frequently useful problem-solving techniques, making this a fabulous resource for education and, most importantly, fun!Features Hundreds of diverting and mathematically interesting problems and puzzles. Accessible for anyone with a high school-level mathematics education. Wonderful resource for teachers and students of mathematics from high school to undergraduate level, and beyond.
API Design for C++
API Design for C++, Second Edition provides a comprehensive discussion of Application Programming Interface (API) development, from initial design through implementation, testing, documentation, release, versioning, maintenance, and deprecation. It is the only book that teaches the strategies of C++ API development, including interface design, versioning, scripting, and plug-in extensibility. Drawing from the author's experience on large scale, collaborative software projects, the text offers practical techniques of API design that produce robust code for the long-term. It presents patterns and practices that provide real value to individual developers as well as organizations. The Second Edition includes all new material fully updated for the latest versions of C++, including a new chapter on concurrency and multithreading, as well as a new chapter discussing how Objective C++ and C++ code can co-exist and how a C++ API can be accessed from Swift programs. In addition, it explores often overlooked issues, both technical and non-technical, contributing to successful design decisions that produce high quality, robust, and long-lived APIs. It focuses on various API styles and patterns that will allow you to produce elegant and durable libraries. A discussion on testing strategies concentrates on automated API testing techniques rather than attempting to include end-user application testing techniques such as GUI testing, system testing, or manual testing.
Spatial Predictive Modeling with R
The book is designed to be very accessible, with a focus on methods, examples, and computing, and theoretical details kept to an absolute minimum. It could be used as a reference for researchers and practitioners in industry. It could also be used as a course text for graduate students of spatial statistics.
Applied Nonlinear Functional Analysis
The second edition covers the introduction to the main mathematical tools of nonlinear functional analysis, which are also used in the study of concrete problems in economics, engineering, and physics. The new edition includes some new topics on Banach spaces of functions and measures and nonlinear analysis.
Statistical Methods for Dynamic Disease Screening and Spatio-Temporal Disease Surveillance
Disease screening and disease surveillance (DSDS) constitute two critical areas in public health, each presenting distinctive challenges primarily due to their sequential decision-making nature and complex data structures. Explores numerous recent analytic methodologies that enhance traditional techniques.
Financial Data Analytics with R
This book is an exploration of statistical methodologies and their applications in finance. Readers are taken on a journey in each chapter through practical explanations and examples, enabling them to develop a solid foundation of these methods in R and their applications in finance.
Change Point Analysis for Time Series
This volume provides a comprehensive survey that covers various modern methods used for detecting and estimating change points in time series and their models. The book primarily focuses on asymptotic theory and practical applications of change point analysis. The methods discussed in the book go beyond the traditional change point methods for univariate and multivariate series. It also explores techniques for handling heteroscedastic series, high-dimensional series, and functional data. While the primary emphasis is on retrospective change point analysis, the book also presents sequential "on-line" methods for detecting change points in real-time scenarios. Each chapter in the book includes multiple data examples that illustrate the practical application of the developed results. These examples cover diverse fields such as economics, finance, environmental studies, and health data analysis. To reinforce the understanding of the material, each chapter concludes with several exercises.Additionally, the book provides a discussion of background literature, allowing readers to explore further resources for in-depth knowledge on specific topics. Overall, "Change Point Analysis for Time Series" offers a broad and informative overview of modern methods in change point analysis, making it a valuable resource for researchers, practitioners, and students interested in analyzing and modeling time series data.
Harmonic Functions and Random Walks on Groups
Research in recent years has highlighted the deep connections between the algebraic, geometric, and analytic structures of a discrete group. New methods and ideas have resulted in an exciting field, with many opportunities for new researchers. This book is an introduction to the area from a modern vantage point. It incorporates the main basics, such as Kesten's amenability criterion, Coulhon and Saloff-Coste inequality, random walk entropy and bounded harmonic functions, the Choquet-Deny Theorem, the Milnor-Wolf Theorem, and a complete proof of Gromov's Theorem on polynomial growth groups. The book is especially appropriate for young researchers, and those new to the field, accessible even to graduate students. An abundance of examples, exercises, and solutions encourage self-reflection and the internalization of the concepts introduced. The author also points to open problems and possibilities for further research.
Ecosystem Modelling with EwE
This textbook provides a basis for courses in ecosystem modelling based on the Ecopath with Ecosim (EwE) modelling framework and software. EwE is a versatile approach with a low but very long (and gradually steeper) learning curve.The authors have been central to the development of EwE for more than thirty years, and during that time the simple Ecopath mass-balance approach it started with has through the addition of time and spatial-dynamic models, among others, been expanded to become a dynamic toolbox that can be used to address anything from simple fundamental research questions to very complex management and policy questions related to ecosystem based management.It's been a guiding principle throughout the development of EwE to provide an easy-to-access approach that does not require extensive mathematical or programming capabilities to get start. Model first, ask later is the philosophy. By just getting started with modelling, you gain insight and can start asking fundamental questions about how components of ecosystems interplay. Diving deeper is important, but this textbook makes the initial getting-started as simple and accessible as possible.
Probability Theory
This book is intended as an introduction to Probability Theory and Mathematical Statistics for students in mathematics, the physical sciences, engineering, and related fields. It is based on the author's 25 years of experience teaching probability and is squarely aimed at helping students overcome common difficulties in learning the subject. The focus of the book is an explanation of the theory, mainly by the use of many examples. Whenever possible, proofs of stated results are provided. All sections conclude with a short list of problems. The book also includes several optional sections on more advanced topics. This textbook would be ideal for use in a first course in Probability Theory. Contents: ProbabilitiesConditional Probabilities and IndependenceRandom Variables and Their DistributionOperations on Random VariablesExpected Value, Variance, and CovarianceNormally Distributed Random VectorsLimit Theorems Introduction to Stochastic ProcessesMathematical StatisticsAppendixBibliographyIndex
Practical Machine Learning with R
This textbook is a comprehensive guide to machine learning and artificial intelligence tailored for students in business and economics. It takes a hands-on approach to teach machine learning, emphasizing practical applications over complex mathematical concepts. Students are not required to have advanced mathematics knowledge such as matrix algebra or calculus.The author introduces machine learning algorithms, utilizing the widely used R language for statistical analysis. Each chapter includes examples, case studies, and interactive tutorials to enhance understanding. No prior programming knowledge is needed. The book leverages the tidymodels package, an extension of R, to streamline data processing and model workflows. This package simplifies commands, making the logic of algorithms more accessible by minimizing programming syntax hurdles. The use of tidymodels ensures a unified experience across various machine learning models.With interactive tutorials that students can download and follow along at their own pace, the book provides a practical approach to apply machine learning algorithms to real-world scenarios.In addition to the interactive tutorials, each chapter includes a Digital Resources section, offering links to articles, videos, data, and sample R code scripts. A companion website further enriches the learning and teaching experience: https: //ai.lange-analytics.com.This book is not just a textbook; it is a dynamic learning experience that empowers students and instructors alike with a practical and accessible approach to machine learning in business and economics. Key Features: Unlocks machine learning basics without advanced mathematics -- no calculus or matrix algebra required. Demonstrates each concept with R code and real-world data for a deep understanding -- no prior programming knowledge is needed. Bridges the gap between theory and real-world applications with hands-on interactive projects and tutorials in every chapter, guided with hints and solutions. Encourages continuous learning with chapter-specific online resources--video tutorials, R-scripts, blog posts, and an online community. Supports instructors through a companion website that includes customizable materials such as slides and syllabi to fit their specific course needs.
A Technical Guide to Mathematical Finance
This book covers those mathematical topics most important to an aspiring or professional quant. The text goes beyond a simple recitation of methods and aims to impart a genuine understanding of the fundamental concepts underpinning most of the techniques and tools routinely used by those working in quantitative finance.
Encounters with Chaos and Fractals
Encounters with Chaos and Fractals, Third Edition provides an accessible introduction to chaotic dynamics and fractal geometry. It incorporates important mathematical concepts and backs up the definitions and results with motivation, examples, and applications.
Mathematical Puzzles
Research in maths is much more than solving puzzles, but most people will agree that solving puzzles is not just fun: it helps focus the mind and increases one's armory of techniques for doing maths. This book makes this connection explicit by isolating important mathematical methods, then using them to solve puzzles and prove a theorem.
Mathematical Puzzles
Research in maths is much more than solving puzzles, but most people will agree that solving puzzles is not just fun: it helps focus the mind and increases one's armory of techniques for doing maths. This book makes this connection explicit by isolating important mathematical methods, then using them to solve puzzles and prove a theorem.
Topics in Model Theory
This book has two chapters. The first is a modern or contemporary account of stability theory. A focus is on the local (formula-by-formula) theory, treated a little differently from in the author's book Geometric Stability Theory. There is also a survey of general and geometric stability theory, as well as applications to combinatorics (stable regularity lemma) using pseudofinite methods.The second is an introduction to 'continuous logic' or 'continuous model theory, ' drawing on the main texts and papers, but with an independent point of view. This chapter includes some historical background, including some other formalisms for continuous logic and a discussion of hyperimaginaries in classical first order logic.These chapters are based around notes, written by students, from a couple of advanced graduate courses in the University of Notre Dame, in Autumn 2018, and Spring 2021.
Topics in Model Theory
This book has two chapters. The first is a modern or contemporary account of stability theory. A focus is on the local (formula-by-formula) theory, treated a little differently from in the author's book Geometric Stability Theory. There is also a survey of general and geometric stability theory, as well as applications to combinatorics (stable regularity lemma) using pseudofinite methods.The second is an introduction to 'continuous logic' or 'continuous model theory, ' drawing on the main texts and papers, but with an independent point of view. This chapter includes some historical background, including some other formalisms for continuous logic and a discussion of hyperimaginaries in classical first order logic.These chapters are based around notes, written by students, from a couple of advanced graduate courses in the University of Notre Dame, in Autumn 2018, and Spring 2021.
Model-Based Monitoring and Statistical Control
Available in English for the first time, this classic and influential book by the late Kohei Otshu presents real examples of ships in motion under irregular ocean waves, helping to expalin fluctuations of stochastic phenomena through spectral analysis methods and statistical modeling.
Causal Inference in Pharmaceutical Statistics
Causal Inference in Pharmaceutical Statistics introduces the basic concepts and fundamental methods of causal inference relevant to pharmaceutical statistics. This book covers causal thinking for different types of commonly used study designs in the pharmaceutical industry, including but not limited to randomized controlled clinical trials, longitudinal studies, singlearm clinical trials with external controls, and real-world evidence studies. The book starts with the central questions in drug development and licensing, takes the reader through the basic concepts and methods via different study types and through different stages, and concludes with a roadmap to conduct causal inference in clinical studies. The book is intended for clinical statisticians and epidemiologists working in the pharmaceutical industry. It will also be useful to graduate students in statistics, biostatistics, and data science looking to pursue a career in the pharmaceutical industry.Key Features: Causal inference book for clinical statisticians in the pharmaceutical industry Introductory level on the most important concepts and methods Align with FDA and ICH guidance documents Across different stages of clinical studies: plan, design, conduct, analysis, and interpretation Cover a variety of commonly used study designs
Ordinal Data Analysis
This book is a step-by-step data story for analysing ordinal data from start to finish. The book is for researchers, statisticians and scientists who are working with data sets where the response is ordinal. This type of data is common in many disciplines, not just in surveys.
The Polls Weren't Wrong
This book will equip readers with the tools to navigate the mismatch of expectations. It is not intended to replace more technical applications of statistics but is accessible to those interested in learning about how poll data should be understood.
Nonparametric Statistical Methods Using R
This thoroughly updated and expanded second edition covers traditional nonparametric methods and rank-based analyses. Two new chapters covering multivariate analyses and big data have been added. Core classical nonparametrics chapters on one- and two-sample problems have been expanded
Simulation and Statistics with Excel
Simulation and Statistics with Excel: An Introduction to Business Students uses a versatile and accessible resource, the Microsoft Excel spreadsheet, to cover the concepts essential to understanding the basic principles and approaches of statistical simulation
Nonlinear Second Order Elliptic Equations
This book focuses on the following three topics in the theory of boundary value problems of nonlinear second order elliptic partial differential equations and systems: (i) eigenvalue problem, (ii) upper and lower solutions method, (iii) topological degree method, and deals with the existence of solutions, more specifically non-constant positive solutions, as well as the uniqueness, stability and asymptotic behavior of such solutions.While not all-encompassing, these topics represent major approaches to the theory of partial differential equations and systems, and should be of significant interest to graduate students and researchers. Two appendices have been included to provide a good gauge of the prerequisites for this book and make it reasonably self-contained.A notable strength of the book is that it contains a large number of substantial examples. Exercises for the reader are also included. Therefore, this book is suitable as a textbook for graduate students who havealready had an introductory course on PDE and some familiarity with functional analysis and nonlinear functional analysis, and as a reference for researchers.
