Diffusion Processes, Jump Processes, and Stochastic Differential Equations
This book provides a compact exposition of the results explaining interrelations between diffusion stochastic processes, SDEs and the fractional infinitesimal operators. The draft of this book has been extensively classroom tested by the author at CWRU in a course that enrolled seniors and graduate students.
Theory of Statistical Inference
The purpose of applying mathematical theory to the theory of statistical inference is to make it simpler and more elegant. Theory of Statistical Inference is concerned with the development of a type of optimization theory which can be used to inform the choice of statistical methodology.
The Book of Proposition Bets
In the modern world the theory of probability is used extensively in mathematics, science, engineering, medicine and, of course, gambling. A proposition bet is one that involves the use of probability -both estimated and actual -where an individual makes an apparently attractive bet to someone who is easily deceived by the odds, which are at first glance in his favor. The Book of Proposition Bets gathers together, and reveals the true mathematics behind, over 50 classic and original proposition bets. From the famous Three Card Monty (really an exercise in the Monty Hall Paradox), to probabilities based on rolling dice and pulling playing cards, or whether or not a mark can guess 3 correct digits of a one dollar bill's serial number (spoiler: the odds are against it), author Owen O'Shea here compiles a fascinating and engaging survey of prop bets. In addition, Part 2 of the book contains a brief history of the theory of probability and some examples of cons and scams perpetrated on the general public to this day around the world, (plus a few more mathematical proposition bets!). Whether to learn the intricacies used by hustlers, or borrow a couple of tricks for yourself, we wager that there is a high probability that readers will enjoy this entertaining and illuminating book!
Counterexamples in Measure and Integration
Often it is more instructive to know 'what can go wrong' and to understand 'why a result fails' than to plod through yet another piece of theory. In this text, the authors gather more than 300 counterexamples - some of them both surprising and amusing - showing the limitations, hidden traps and pitfalls of measure and integration. Many examples are put into context, explaining relevant parts of the theory, and pointing out further reading. The text starts with a self-contained, non-technical overview on the fundamentals of measure and integration. A companion to the successful undergraduate textbook Measures, Integrals and Martingales, it is accessible to advanced undergraduate students, requiring only modest prerequisites. More specialized concepts are summarized at the beginning of each chapter, allowing for self-study as well as supplementary reading for any course covering measures and integrals. For researchers, it provides ample examples and warnings as to the limitations of general measure theory. This book forms a sister volume to Ren矇 Schilling's other book Measures, Integrals and Martingales (www.cambridge.org/9781316620243).
Advanced R Solutions
This book offers solutions to all 284 exercises in Advanced R, Second Edition. All the solutions have been carefully documented and made to be as clear and accessible as possible.
Mathematics of the Big Four Casino Table Games
Mathematics is the basis of casino games, which are the bedrock of a $100 billion/year industry. Mathematics of the Big Four Casino Table Games: Blackjack, Baccarat, Craps, & Roulette takes an in-depth look at the four biggest table games in casinos: blackjack, baccarat, craps, and roulette. It guides readers through the mathematical principles that underpin these games and their different variations, providing insights that will be of huge interest to gamblers, casino managers, researchers, and students of mathematics.Features A valuable teaching resource, replete with exercises, for any course on gambling mathematics Suitable for a wide audience of professionals, researchers, and students Many practical applications for the gambling industry Mark Bollman is Professor of Mathematics and chair of the Department of Mathematics & Computer Science at Albion College in Albion, Michigan, and has taught 116 different courses in his career. Among these courses is "Mathematics of the Gaming Industry," where mathematics majors carefully study the math behind games of chance and travel to Las Vegas, Nevada, in order to compare theory and practice. He has also taken those ideas into Albion's Honors Program in "Great Issues in Humanities: Perspectives on Gambling," which considers gambling from literary, philosophical, and historical points of view as well as mathematically. Mark has also authored Basic Gambling Mathematics: The Numbers Behind the Neon, Mathematics of Keno and Lotteries, and Mathematics of Casino Carnival Games.
Counterexamples in Measure and Integration
Often it is more instructive to know 'what can go wrong' and to understand 'why a result fails' than to plod through yet another piece of theory. In this text, the authors gather more than 300 counterexamples - some of them both surprising and amusing - showing the limitations, hidden traps and pitfalls of measure and integration. Many examples are put into context, explaining relevant parts of the theory, and pointing out further reading. The text starts with a self-contained, non-technical overview on the fundamentals of measure and integration. A companion to the successful undergraduate textbook Measures, Integrals and Martingales, it is accessible to advanced undergraduate students, requiring only modest prerequisites. More specialized concepts are summarized at the beginning of each chapter, allowing for self-study as well as supplementary reading for any course covering measures and integrals. For researchers, it provides ample examples and warnings as to the limitations of general measure theory. This book forms a sister volume to Ren矇 Schilling's other book Measures, Integrals and Martingales (www.cambridge.org/9781316620243).
Calculus Set Free
Calculus Set Free: Infinitesimals to the Rescue is a single-variable calculus textbook that incorporates the use of infinitesimal methods. The procedures used throughout make many of the calculations simpler and the concepts clearer for undergraduate students, heightening success and easing a significant burden of entry into STEM disciplines. This text features a student-friendly exposition with ample marginal notes, examples, illustrations, and more. The exercises include a wide range of difficulty levels, stretching from very simple "rapid response" questions to the occasional exercise meant to test knowledge. While some exercises require the use of technology to work through, none are dependent on any specific software. The answers to odd-numbered exercises in the back of the book include both simplified and non-simplified answers, hints, or alternative answers. Throughout the text, notes in the margins include comments meant to supplement understanding, sometimes including line-by-line commentary for worked examples. Without sacrificing academic rigor, Calculus Set Free offers an engaging style that helps students to solidify their understanding on difficult theoretical calculus.
Advanced Statistics for Testing Assumed Causal Relationships
This book concentrates on linear regression, path analysis and logistic regressions, the most used statistical techniques for the test of causal relationships. Its emphasis is on the conceptions and applications of the techniques by using simple examples without requesting any mathematical knowledge. It shows multiple regression analysis accurately reconstructs the causal relationships between phenomena. So, it can be used to test the hypotheses about causal relationships between variables. It presents that potential effects of each independent variable on the dependent variable are not limited to direct and indirect effects. The path analysis shows each independent variable has a pure effect on the dependent variable. So, it can be shown the unique contribution of each independent variable to the variation of the dependent variable. It is an advanced statistical text for the graduate students in social and behavior sciences. It also serves as a reference for professionals and researchers.
Bioinformatics and RNA
This book offers a unique balance between a basic introductory knowledge of bioinformatics and a detailed study of algorithmic techniques. Bioinformatics and RNA: A Practice-Based Approach is a complete guide on the fundamental concepts, applications, algorithms, protocols, new trends, challenges, and research results in the area of bioinformatics and RNA. The book offers a broad introduction to the explosively growing new discipline of bioinformatics. It covers theoretical topics along with computational algorithms. It explores RNA bioinformatics, which contribute to therapeutics and drug discovery. Implementation of algorithms in a DotNet Framework with code and complete insight on the state-of-the-art and recent advancements are presented in detail. The book targets both novice readers as well as practitioners in the field. FEATURES Offers a broad introduction to the explosively growing new discipline of bioinformatics Covers theoretical topics and computational algorithms Explores RNA bioinformatics to unleash the potential from therapeutics to drug discovery Discusses implementation of algorithms in DotNet Frameworks with code Presents insights into the state of the art and recent advancements in bioinformatics The book is useful to undergraduate students with engineering, science, mathematics, or biology backgrounds. Researchers will be equally interested.
Bootstrap Methods
This book provides a compact introduction to the bootstrap method. In addition to classical results on point estimation and test theory, multivariate linear regression models and generalized linear models are covered in detail. Special attention is given to the use of bootstrap procedures to perform goodness-of-fit tests to validate model or distributional assumptions. In some cases, new methods are presented here for the first time. The text is motivated by practical examples and the implementations of the corresponding algorithms are always given directly in R in a comprehensible form. Overall, R is given great importance throughout. Each chapter includes a section of exercises and, for the more mathematically inclined readers, concludes with rigorous proofs. The intended audience is graduate students who already have a prior knowledge of probability theory and mathematical statistics.
Brownian Motion
Stochastic processes occur everywhere in the sciences, economics and engineering, and they need to be understood by (applied) mathematicians, engineers and scientists alike. This book gives a gentle introduction to Brownian motion and stochastic processes, in general. Brownian motion plays a special role, since it shaped the whole subject, displays most random phenomena while being still easy to treat, and is used in many real-life models. Im this new edition, much material is added, and there are new chapters on ''Wiener Chaos and Iterated It繫 Integrals'' and ''Brownian Local Times''.
Stochastik Ohne Zufall Und Wahrscheinlichkeit
In diesem Buch wird Grundlegendes der Stochastik wie Kolmogoroffsche Axiome, Erwartungswerte, bedingte Wahrscheinlichkeiten, stochastische Unabh瓣ngigkeit, Satz von Bayes oder Satz von der totalen Wahrscheinlichkeit nicht mit "Zufall" und "Wahrscheinlichkeit", sondern mit "relativer Anteil" formuliert. Drei Interpretationen relativer Anteile werden n瓣her betrachtet: Freude, Macht und Wahrscheinlichkeit. Anhand vieler Beispiele wird gezeigt, dass die angewandte Stochastik nicht nur allgemeiner und umfassender, sondern auch einfacher und anschaulicher wird, wenn man sie auf relativen Anteilen statt auf Zufall und Wahrscheinlichkeit aufbaut.
Chance, Logic and Intuition
Chance rules our daily lives in many different ways. From the outcomes of the lottery to the outcomes of medical tests, from the basketball court to the court of law. The ways of chance are capricious. Bizarre things happen all the time. Nevertheless, chance has a logic of its own. It obeys the rules of probability. But if you open a standard book on probability, you may very well feel far removed from everyday life. Abstract formulas and mathematical symbols stare back at you with almost every turn of the page.This book introduces you to the logic of chance without the use of mathematical formulas or symbols. In Part One, you will meet the fascinating pioneers of the mathematics of probability, including Galileo Galilei and Blaise Pascal. Their stories will introduce you, step by step, to the basics of probability. In Part Two, various examples in all areas of daily life will show you how chance defies our expectations time and again. But armed with the basic rules of probability and a good dose of inventiveness, you will be able to unravel the counter-intuitive logic of chance.
One-Dimensional Dynamical Systems
For almost every phenomenon in Physics, Chemistry, and other sciences one can make a mathematical model that can be regarded as a dynamical system. This book seeks to deep-dive into α standard maps as an example-driven way of explaining the modern theory of the subject in a way that will be engaging for students.
Nonlinear Valuation and Non-Gaussian Risks in Finance
What happens to risk as the economic horizon goes to zero and risk is seen as an exposure to a change in state that may occur instantaneously at any time? All activities that have been undertaken statically at a fixed finite horizon can now be reconsidered dynamically at a zero time horizon, with arrival rates at the core of the modeling. This book, aimed at practitioners and researchers in financial risk, delivers the theoretical framework and various applications of the newly established dynamic conic finance theory. The result is a nonlinear non-Gaussian valuation framework for risk management in finance. Risk-free assets disappear and low risk portfolios must pay for their risk reduction with negative expected returns. Hedges may be constructed to enhance value by exploiting risk interactions. Dynamic trading mechanisms are synthesized by machine learning algorithms. Optimal exposures are designed for option positioning simultaneously across all strikes and maturities.
Canard Cycles
This book offers the first systematic account of canard cycles, an intriguing phenomenon in the study of ordinary differential equations. The canard cycles are treated in the general context of slow-fast families of two-dimensional vector fields. The central question of controlling the limit cycles is addressed in detail and strong results are presented with complete proofs.In particular, the book provides a detailed study of the structure of the transitions near the critical set of non-isolated singularities. This leads to precise results on the limit cycles and their bifurcations, including the so-called canard phenomenon and canard explosion. The book also provides a solid basis for the use of asymptotic techniques. It gives a clear understanding of notions like inner and outer solutions, describing their relation and precise structure.The first part of the book provides a thorough introduction to slow-fast systems, suitable for graduate students. The second and third parts will be of interest to both pure mathematicians working on theoretical questions such as Hilbert's 16th problem, as well as to a wide range of applied mathematicians looking for a detailed understanding of two-scale models found in electrical circuits, population dynamics, ecological models, cellular (FitzHugh-Nagumo) models, epidemiological models, chemical reactions, mechanical oscillators with friction, climate models, and many other models with tipping points.
Characters of Groups and Lattices Over Orders
This is the fi rst textbook leading coherently from classical character theory to the theory of lattices over orders and integral representations of fi nite groups. Character theory is developed in a highly pedagogical way including many examples and exercises covering at once the fi rst defi nitions up to Clifford theory, Brauer's induction theorem and the splitting fi eld theorem, as well as self-dual simple modules allowing bilinear forms. This latter part is done step by step using the approach given by Sin and Willems. Dirichlet characters and Dirichlet's result on primes in arithmetic progressions are given as an application. Examples of integral representations of fi nite groups are already detailed at a quite early stage where appropriate, so that the more systematic treatment of lattices over orders is natural. After that, the necessary number theory and homological algebra is developed as far as needed. Maximal as well as hereditary orders are introduced and the Auslander- Buchsbaum theorem is proved. The Jordan-Zassenhaus theorem on the fi niteness of lattices in a given vector space is fully proved. Then the development and properties of class groups of orders is a fi rst focus. As a further highlight Swan's example of a stably free but not free ideal over the integral group ring of the generalised quaternion group of order 32 is developed in great detail. A student friendly introduction to ordinary representation theory Many examples and exercises, including solutions for some of them, make the book well suited for self-study Leads coherently from ordinary character theory to the integral representation theory of lattices over orders Several topics appear for the fi rst time in a textbook, such as Sin-Willems' approach to self-dual simple modules and Swan's example of a stably free non free ideal.
Smooth Functions and Maps
The book contains a consistent and sufficiently comprehensive theory of smooth functions and maps insofar as it is connected with differential calculus. The scope of notions includes, among others, Lagrange inequality, Taylor's formula, finding absolute and relative extrema, theorems on smoothness of the inverse map and on conditions of local invertibility, implicit function theorem, dependence and independence of functions, classification of smooth functions up to diffeomorphism. The concluding chapter deals with a more specific issue of critical values of smooth mappings. In several chapters, a relatively new technical approach is used that allows the authors to clarify and simplify some of the technically difficult proofs while maintaining full integrity. Besides, the book includes complete proofs of some important results which until now have only been published in scholarly literature or scientific journals (remainder estimates of Taylor's formula in a nonconvex area (Chapter I, 禮8), Whitney's extension theorem for smooth function (Chapter I, 禮11) and some of its corollaries, global diffeomorphism theorem (Chapter II, 禮5), results on sets of critical values of smooth mappings and the related Whitney example (Chapter IV). The text features multiple examples illustrating the results obtained and demonstrating their accuracy. Moreover, the book contains over 150 problems and 19 illustrations. Perusal of the book equips the reader to further explore any literature basing upon multivariable calculus.
Multivariate Analysis for the Behavioral Sciences, Second Edition
Multivariate Analysis for the Behavioral Sciences, Second Edition is designed to show how a variety of statistical methods can be used to analyse data collected by psychologists and other behavioral scientists.
Nonlinear Optimization
The study of nonlinear optimization is both fundamental and a key course for applied mathematics, operations research, management science, industrial engineering, and economics at most colleges and universities.
Limit Distributions for Sums of Independent Random Variables
2021 Reprint of the 1954 Edition. Facsimile of the original edition and not reproduced with Optical Recognition. This treatise on the fundamental limit theorems in probability theory is strong on mathematical rigor, but the presentation is equally distinguished by clarity and elegance. With broad perspectives on the development from the law of large numbers (Bernoulli, 1713) and the limit theorems of de Moivre (1730), Laplace (1812), and Poisson (1837), over the important progress made by Chebyshev (1867, 1890), Lyapunov (1901), and Lindeberg (1922), the book focuses on the progress experts had made on the subject up to the time of publication. This book may be considered a genuine classic.Of general interest is the material in the two first chapters, which may serve as a basis for any rigorous course in probability theory. The axiomatic foundation of the theory given by Kolmogorov in 1933 is here somewhat modified, the probability distributions being specified so as to form a perfect measure, a restriction which removes certain intricacies, notably in the treatment of conditional probabilities and expectations. The careful translation is based on the Russian original (1949. The two appendixes and some fifty extra footnotes give clarifying and instructive remarks.
Markov Processes for Stochastic Modeling
This book presents an algebraic development of the theory of countable state space Markov chains with discrete- and continuous-time parameters. A Markov chain is a stochastic process characterized by the Markov prop- erty that the distribution of future depends only on the current state, not on the whole history. Despite its simple form of dependency, the Markov property has enabled us to develop a rich system of concepts and theorems and to derive many results that are useful in applications. In fact, the areas that can be modeled, with varying degrees of success, by Markov chains are vast and are still expanding. The aim of this book is a discussion of the time-dependent behavior, called the transient behavior, of Markov chains. From the practical point of view, when modeling a stochastic system by a Markov chain, there are many instances in which time-limiting results such as stationary distributions have no meaning. Or, even when the stationary distribution is of some importance, it is often dangerous to use the stationary result alone without knowing the transient behavior of the Markov chain. Not many books have paid much attention to this topic, despite its obvious importance.
Inhomogeneous Random Evolutions and Their Applications
Inhomogeneous Random Evolutions and Their Applications explains how to model various dynamical systems in finance and insurance with non-homogeneous in time characteristics. It includes modeling for: financial underlying and derivatives via Levy processes with time-dependent characteristics;limit order books in the algorithmic and HFT with counting price changes processes having time-dependent intensities;risk processes which count number of claims with time-dependent conditional intensities;multi-asset price impact from distressed selling;regime-switching Levy-driven diffusion-based price dynamics.Initial models for those systems are very complicated, which is why the author's approach helps to simplified their study. The book uses a very general approach for modeling of those systems via abstract inhomogeneous random evolutions in Banach spaces. To simplify their investigation, it applies the first averaging principle (long-run stability property or law of large numbers [LLN]) to get deterministic function on the long run. To eliminate the rate of convergence in the LLN, it uses secondly the functional central limit theorem (FCLT) such that the associated cumulative process, centered around that deterministic function and suitably scaled in time, may be approximated by an orthogonal martingale measure, in general; and by standard Brownian motion, in particular, if the scale parameter increases. Thus, this approach allows the author to easily link, for example, microscopic activities with macroscopic ones in HFT, connecting the parameters driving the HFT with the daily volatilities. This method also helps to easily calculate ruin and ultimate ruin probabilities for the risk process. All results in the book are new and original, and can be easily implemented in practice.
Dynamic Treatment Regimes
Precision medicine seeks to use data to construct principled, i.e., evidence-based, treatment strategies that dictate where, when, and to whom treatment should be applied. This book provides an accessible yet comprehensive introduction to statistical methodology for dynamic treatment regimes.
Vagueness in the Exact Sciences
The book starts with the assumption that vagueness is a fundamental property of this world. From a philosophical account of vagueness via the presentation of alternative mathematics of vagueness, the subsequent chapters explore how vagueness manifests itself in the various exact sciences: physics, chemistry, biology, medicine, computer science, and engineering.
Special Functions and Their Applications
Special functions are mathematical functions that have established names and notations due to their importance in mathematical analysis, functional analysis, geometry, physics, or other applications. This short text gives clear descriptions and explanations of the Gamma function, the Probability Integral and its related functions, Spherical Harmonics Theory, The Bessel function, Hermite polynomials and Laguerre polynomials. Each chapter finishes with a description of how the function is most commonly applied and a set of examples for the student to work through.
Synchronization in Infinite-Dimensional Deterministic and Stochastic Systems
The main goal of this book is to systematically address the mathematical methods that are applied in the study of synchronization of infinite-dimensional evolutionary dissipative or partially dissipative systems. It bases its unique monograph presentation on both general and abstract models and covers several important classes of coupled nonlinear deterministic and stochastic PDEs which generate infinite-dimensional dissipative systems. This text, which adapts readily to advanced graduate coursework in dissipative dynamics, requires some background knowledge in evolutionary equations and introductory functional analysis as well as a basic understanding of PDEs and the theory of random processes. Suitable for researchers in synchronization theory, the book is also relevant to physicists and engineers interested in both the mathematical background and the methods for the asymptotic analysis of coupled infinite-dimensional dissipative systems that arise in continuum mechanics.
Interpretative Aspects of Quantum Mechanics
This book presents a selection of Prof. Matteo Campanella's writings on the interpretative aspects of quantum mechanics and on a possible derivation of Born's rule - one of the key principles of the probabilistic interpretation of quantum mechanics - that is independent of any priori probabilistic interpretation. This topic is of fundamental interest, and as such is currently an active area of research. Starting from a natural method of defining such a state, Campanella found that it can be characterized through a partial density operator, which occurs as a consequence of the formalism and of a number of reasonable assumptions connected with the notion of a state. The book demonstrates that the density operator arises as an orbit invariant that has to be interpreted as probabilistic, and that its quantitative implementation is equivalent to Born's rule. The appendices present various mathematical details, which would have interrupted the continuity of the discussion if they had been included in the main text. For instance, they discuss baricentric coordinates, mapping between Hilbert spaces, tensor products between linear spaces, orbits of vectors of a linear space under the action of its structure group, and the class of Hilbert space as a category.
Bayes Rules!
An engaging, sophisticated, and fun introduction to the field of Bayesian statistics, Bayes Rules!: An Introduction to Applied Bayesian Modeling brings the power of modern Bayesian thinking, modeling, and computing to a broad audience. In particular, the book is an ideal resource for advanced undergraduate statistics students and practitioners with comparable experience. the book assumes that readers are familiar with the content covered in a typical undergraduate-level introductory statistics course. Readers will also, ideally, have some experience with undergraduate-level probability, calculus, and the R statistical software. Readers without this background will still be able to follow along so long as theyare eager to pick up these tools on the fly as all R code is provided.Bayes Rules! empowers readers to weave Bayesian approaches into their everyday practice. Discussions and applications are data driven. A natural progression from fundamental to multivariable, hierarchical models emphasizes a practical and generalizable model building process. The evaluation of these Bayesian models reflects the fact that a data analysis does not exist in a vacuum.Features- Utilizes data-driven examples and exercises.- Emphasizes the iterative model building and evaluation process.- Surveys an interconnected range of multivariable regression and classification models.- Presents fundamental Markov chain Monte Carlo simulation.- Integrates R code, including RStan modeling tools and the bayesrules package.- Encourages readers to tap into their intuition and learn by doing.- Provides a friendly and inclusive introduction to technical Bayesian concepts.- Supports Bayesian applications with foundational Bayesian theory.
Introduction to Quantum Control and Dynamics
The introduction of control theory in quantum mechanics has created a rich, new interdisciplinary scientific field, which is producing novel insight into important theoretical questions at the heart of quantum physics.
An Invitation to Unbounded Representations of ∗-Algebras on Hilbert Space
General Notation.- 1 Prologue: The Algebraic Approach to Quantum Theories.- 2 ∗-Algebras.- 3 O*-Algebras.- 4 ∗-Representations.- 5 Positive Linear Functionals.- 6 Representations of Tensor Algebras.- 7 Integrable Representations of Commutative ∗-Algebras.- 8 The Weyl Algebra and the Canonical Commutation Relation.- 9 Integrable Representations of Enveloping Algebras.- 10 Archimedean Quadratic Modules and Positivstellens瓣tze.- 11 The Operator Relation XX*=F(X*X).- 12 Induced ∗-Representations.- 13 Well-behaved ∗-Representations.- 14 Representations on Rigged Spaces and Hilbert C*-modules. A Unbounded Operators on Hilbert Space.- B C*-Algebras and Representations.- C Locally Convex Spaces and Separation of Convex Sets.- References.- Symbol Index.- Subject Index.
Handbook of Multiple Comparisons
Written by experts that include originators of some key ideas, chapters in the Handbook of Multiple Testing cover multiple comparison problems big and small, with guidance toward error rate control and insights on how principles developed earlier can be applied to current and emerging problems. Some highlights of the coverages are as follows.Error rate control is useful for controlling the incorrect decision rate. Chapter 1 introduces Tukey's original multiple comparison error rates and point to how they have been applied and adapted to modern multiple comparison problems as discussed in the later chapters. Principles endure. While the closed testing principle is more familiar, Chapter 4 shows the partitioning principle can derive confidence sets for multiple tests, which may become important as the profession goes beyond making decisions based on p-values.Multiple comparisons of treatment efficacy often involve multiple doses and endpoints. Chapter 12 on multiple endpoints explains how different choices of endpoint types lead to different multiplicity adjustment strategies, while Chapter 11 on the MCP-Mod approach is particularly useful for dose-finding. To assess efficacy in clinical trials with multiple doses and multiple endpoints, the reader can see the traditional approach in Chapter 2, the Graphical approach in Chapter 5, and the multivariate approach in Chapter 3. Personalized/precision medicine based on targeted therapies, already a reality, naturally leads to analysis of efficacy in subgroups. Chapter 13 draws attention to subtle logical issues in inferences on subgroups and their mixtures, with a principled solution that resolves these issues. This chapter has implication toward meeting the ICHE9R1 Estimands requirement.Besides the mere multiple testing methodology itself, the handbook also covers related topics like the statistical task of model selection in Chapter 7 or the estimation of the proportion of true null hypotheses (or, in other words, the signal prevalence) in Chapter 8. It also contains decision-theoretic considerations regarding the admissibility of multiple tests in Chapter 6. The issue of selected inference is addressed in Chapter 9.Comparison of responses can involve millions of voxels in medical imaging or SNPs in genome-wide association studies (GWAS). Chapter 14 and Chapter 15 provide state of the art methods for large scale simultaneous inference in these settings.
Logistische Regression
Dieses Open-Access-Buch gibt eine anwendungsorientierte Einf羹hrung in die logistische Regression. Ausgehend von Grundkenntnissen der linearen Regression wird diese zuerst als zweistufiges Modell interpretiert, was den ?bergang zur logistischen Regression vereinfacht. Neben einer kompakten Einf羹hrung der entsprechenden Theorie liegt der Fokus auch auf der Umsetzung mit der Statistiksoftware R und der richtigen Formulierung der entsprechenden Ergebnisse. Alle Schritte werden anhand zahlreicher Beispiele illustriert. Hinzu kommt eine Einf羹hrung in die Klassifikation mit den entsprechenden Begriffen.
Practical Numerical Mathematics with MATLAB
This workbook is intended for advanced undergraduate or beginning graduate students as a supplement to a traditional course in numerical mathematics and as preparation for independent research involving numerical mathematics. Upon completion of this workbook, students will have a working knowledge of MATLAB programming, they will have themselves programmed algorithms encountered in classwork and textbooks, and they will know how to check and verify their own programs against hand calculations and by reference to theoretical results, special polynomial solutions and other specialized solutions. No previous programming experience with MATLAB is necessary.
Practical Numerical Mathematics with MATLAB
This workbook and solutions manual is intended for advanced undergraduate or beginning graduate students as a supplement to a traditional course in numerical mathematics and as preparation for independent research involving numerical mathematics. The solutions manual provides complete MATLAB code and numerical results for each of the exercises in the workbook and will be especially useful for those students without previous MATLAB programming experience. It is also valuable for classroom instructors to help pinpoint the author's intent in each exercise and to provide a model for graders. Upon completion of this material, students will have a working knowledge of MATLAB programming, they will have themselves programmed algorithms encountered in classwork and textbooks, and they will know how to check and verify their own programs against hand calculations and by reference to theoretical results, special polynomial solutions and other specialized solutions. No previous programming experience with MATLAB is necessary.
Point Processes and Jump Diffusions
The theory of marked point processes on the real line is of great and increasing importance in areas such as insurance mathematics, queuing theory and financial economics. However, the theory is often viewed as technically and conceptually difficult and has proved to be a block for PhD students looking to enter the area. This book gives an intuitive picture of the central concepts as well as the deeper results, while presenting the mathematical theory in a rigorous fashion and discussing applications in filtering theory and financial economics. Consequently, readers will get a deep understanding of the theory and how to use it. A number of exercises of differing levels of difficulty are included, providing opportunities to put new ideas into practice. Graduate students in mathematics, finance and economics will gain a good working knowledge of point-process theory, allowing them to progress to independent research.
Practical Numerical Mathematics with MATLAB
This workbook and solutions manual is intended for advanced undergraduate or beginning graduate students as a supplement to a traditional course in numerical mathematics and as preparation for independent research involving numerical mathematics. The solutions manual provides complete MATLAB code and numerical results for each of the exercises in the workbook and will be especially useful for those students without previous MATLAB programming experience. It is also valuable for classroom instructors to help pinpoint the author's intent in each exercise and to provide a model for graders. Upon completion of this material, students will have a working knowledge of MATLAB programming, they will have themselves programmed algorithms encountered in classwork and textbooks, and they will know how to check and verify their own programs against hand calculations and by reference to theoretical results, special polynomial solutions and other specialized solutions. No previous programming experience with MATLAB is necessary.
Practical Numerical Mathematics with MATLAB
This workbook and solutions manual is intended for advanced undergraduate or beginning graduate students as a supplement to a traditional course in numerical mathematics and as preparation for independent research involving numerical mathematics. The solutions manual provides complete MATLAB code and numerical results for each of the exercises in the workbook and will be especially useful for those students without previous MATLAB programming experience. It is also valuable for classroom instructors to help pinpoint the author's intent in each exercise and to provide a model for graders. Upon completion of this material, students will have a working knowledge of MATLAB programming, they will have themselves programmed algorithms encountered in classwork and textbooks, and they will know how to check and verify their own programs against hand calculations and by reference to theoretical results, special polynomial solutions and other specialized solutions. No previous programming experience with MATLAB is necessary.
Microeconomic Theory for the Social Sciences
This textbook covers microeconomic theory at the level of intermediate and advanced undergraduates. It is also intended as an introduction for those with other intellectual and academic backgrounds who may not necessarily agree with "mainstream" economists but at least are interested knowing how they think and see things.The book provides thorough explanations of definitions and assumptions that the theory is based upon. It provides comprehensive accounts of motivations and reservations behind the theory. As well, it precisely presents the logical process of how the assumptions lead to the conclusion, conveying the intuition and the key of the arguments. An abundance of topics is included here: individual choice, general equilibrium, partial equilibrium, game theory, imperfect competition, transaction under incomplete information, market failures, welfare economics, social choice and mechanism design. The book is a valuable resource for any reader studying or simply interested in microeconomic theory.
Differentiability in Banach Spaces, Differential Forms and Applications
This book is divided into two parts, the first one to study the theory of differentiable functions between Banach spaces and the second to study the differential form formalism and to address the Stokes' Theorem and its applications. Related to the first part, there is an introduction to the content of Linear Bounded Operators in Banach Spaces with classic examples of compact and Fredholm operators, this aiming to define the derivative of Fr矇chet and to give examples in Variational Calculus and to extend the results to Fredholm maps. The Inverse Function Theorem is explained in full details to help the reader to understand the proof details and its motivations. The inverse function theorem and applications make up this first part. The text contains an elementary approach to Vector Fields and Flows, including the Frobenius Theorem. The Differential Forms are introduced and applied to obtain the Stokes Theorem and to define De Rham cohomology groups. As an application, the finalchapter contains an introduction to the Harmonic Functions and a geometric approach to Maxwell's equations of electromagnetism.
Determining Sample Size and Power in Research Studies
This book addresses sample size and power in the context of research, offering valuable insights for graduate and doctoral students as well as researchers in any discipline where data is generated to investigate research questions. It explains how to enhance the authenticity of research by estimating the sample size and reporting the power of the tests used. Further, it discusses the issue of sample size determination in survey studies as well as in hypothesis testing experiments so that readers can grasp the concept of statistical errors, minimum detectable difference, effect size, one-tail and two-tail tests and the power of the test. The book also highlights the importance of fixing these boundary conditions in enhancing the authenticity of research findings and improving the chances of research papers being accepted by respected journals. Further, it explores the significance of sample size by showing the power achieved in selected doctoral studies. Procedure has been discussed to fix power in the hypothesis testing experiment. One should usually have power at least 0.8 in the study because having power less than this will have the issue of practical significance of findings. If the power in any study is less than 0.5 then it would be better to test the hypothesis by tossing a coin instead of organizing the experiment. It also discusses determining sample size and power using the freeware G*Power software, based on twenty-one examples using different analyses, like t-test, parametric and non-parametric correlations, multivariate regression, logistic regression, independent and repeated measures ANOVA, mixed design, MANOVA and chi-square.
Approximation Theory and Analytic Inequalities
This contributed volume focuses on various important areas of mathematics in which approximation methods play an essential role. It features cutting-edge research on a wide spectrum of analytic inequalities with emphasis on differential and integral inequalities in the spirit of functional analysis, operator theory, nonlinear analysis, variational calculus, featuring a plethora of applications, making this work a valuable resource. The reader will be exposed to convexity theory, polynomial inequalities, extremal problems, prediction theory, fixed point theory for operators, PDEs, fractional integral inequalities, multidimensional numerical integration, Gauss-Jacobi and Hermite-Hadamard type inequalities, Hilbert-type inequalities, and Ulam's stability of functional equations. Contributions have been written by eminent researchers, providing up-to-date information and several results which may be useful to a wide readership including graduate students and researchers working in mathematics, physics, economics, operational research, and their interconnections.
Advanced Analytics with Transact-SQL
Learn about business intelligence (BI) features in T-SQL and how they can help you with data science and analytics efforts without the need to bring in other languages such as R and Python. This book shows you how to compute statistical measures using your existing skills in T-SQL. You will learn how to calculate descriptive statistics, including centers, spreads, skewness, and kurtosis of distributions. You will also learn to find associations between pairs of variables, including calculating linear regression formulas and confidence levels with definite integration. No analysis is good without data quality. Advanced Analytics with Transact-SQL introduces data quality issues and shows you how to check for completeness and accuracy, and measure improvements in data quality over time. The book also explains how to optimize queries involving temporal data, such as when you search for overlapping intervals. More advanced time-oriented information in the book includes hazard and survival analysis. Forecasting with exponential moving averages and autoregression is covered as well. Every web/retail shop wants to know the products customers tend to buy together. Trying to predict the target discrete or continuous variable with few input variables is important for practically every type of business. This book helps you understand data science and the advanced algorithms use to analyze data, and terms such as data mining, machine learning, and text mining.Key to many of the solutions in this book are T-SQL window functions. Author Dejan Sarka demonstrates efficient statistical queries that are based on window functions and optimized through algorithms built using mathematical knowledge and creativity. The formulas and usage of those statistical procedures are explained so you can understand and modify the techniques presented. T-SQL is supported in SQL Server, Azure SQL Database, and in Azure Synapse Analytics. There are so many BI features in T-SQL that it might become your primary analytic database language. If you want to learn how to get information from your data with the T-SQL language that you already are familiar with, then this is the book for you. What You Will LearnDescribe distribution of variables with statistical measuresFind associations between pairs of variablesEvaluate the quality of the data you are analyzingPerform time-series analysis on your dataForecast values of a continuous variablePerform market-basket analysis to predict customer purchasing patternsPredict target variable outcomes from one or more input variablesCategorize passages of text by extracting and analyzing keywords Who This Book Is ForDatabase developers and database administrators who want to translate their T-SQL skills into the world of business intelligence (BI) and data science. For readers who want to analyze large amounts of data efficiently by using their existing knowledge of T-SQL and Microsoft's various database platforms such as SQL Server and Azure SQL Database. Also for readers who want to improve their querying by learning new and original optimization techniques.
Computation and Approximation
This brief studies recent work conducted on certain exponential type operators and other integral type operators. It consists of three chapters: the first on exponential type operators, the second a study of some modifications of linear positive operators, and the third on difference estimates between two operators. It will be of interest to students both graduate and undergraduate studying linear positive operators and the area of approximation theory.
Combinatorial Inference in Geometric Data Analysis
Combinatorial Inference in Geometric Data Analysis gives an overview of multidimensional statistical inference methods applicable to clouds of points that make no assumption on the process of generating data or distributions, and that are not based on random modelling but on permutation procedures recasting in a combinatorial fr
Generalized Linear Models with Random Effects
This is the second edition of a monograph on generalized linear models with random effects that extends the classic work of McCullagh and Nelder. It has been thoroughly updated, with around 80 pages added, including new material on the extended likelihood approach that strengthens the theoretical basis of the methodology, new developments in variable selection and multiple testing, and new examples and applications. It includes an R package for all the methods and examples that supplement the book.
Computational Methods and Experimental Measurements XX
Formed of papers presented at the 20th International Conference on Computational Methods and Experimental Measurements, this volume provides a view of the latest work on the interaction between computational methods and experiments.The continuous improvement in computer efficiency, coupled with diminishing costs and the rapid development of numerical procedures have generated an ever-increasing expansion of computational simulations that permeate all fields of science and technology. As these procedures continue to grow in magnitude and complexity, it is essential to validate their results to be certain of their reliability. This can be achieved by performing dedicated and accurate experiments, which have undergone constant and enormous development. At the same time, current experimental techniques have become more complex and sophisticated so that they require the intensive use of computers, both for running experiments as well as acquiring and processing the resulting data.Some of the subject areas covered are: Fluid flow studies and experiments; Structural and stress analysis; Materials characterization; Electromagnetic problems; Structural integrity; Destructive and non-destructive testing; Heat transfer and thermal processes; Advances in computational methods; Automotive applications; Aerospace applications; Ocean engineering and marine structures; Fluid structure interaction; Bio-electromagnetics; Process simulations; Environmental monitoring, modelling and applications; Validation of computer modelling; Data and signal processing; Virtual testing and verification; Electromagnetic compatibility; Life cycle assessment.
