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Probability for Finance
by Ekkehard Kopp Jan Malczak Tomasz ZastawniakStudents and instructors alike will benefit from this rigorous, unfussy text, which keeps a clear focus on the basic probabilistic concepts required for an understanding of financial market models, including independence and conditioning. Assuming only some calculus and linear algebra, the text develops key results of measure and integration, which are applied to probability spaces and random variables, culminating in central limit theory. Consequently it provides essential prerequisites to graduate-level study of modern finance and, more generally, to the study of stochastic processes. Results are proved carefully and the key concepts are motivated by concrete examples drawn from financial market models. Students can test their understanding through the large number of exercises and worked examples that are integral to the text.
Probability for Information Technology
by Changho SuhThis book introduces probabilistic modelling and explores its role in solving a broad spectrum of engineering problems that arise in Information Technology (IT). Divided into three parts, it begins by laying the foundation of basic probability concepts such as sample space, events, conditional probability, independence, total probability law and random variables. The second part delves into more advanced topics including random processes and key principles like Maximum A Posteriori (MAP) estimation, the law of large numbers and the central limit theorem. The last part applies these principles to various IT domains like communication, social networks, speech recognition, and machine learning, emphasizing the practical aspect of probability through real-world examples, case studies, and Python coding exercises. A notable feature of this book is its narrative style, seamlessly weaving together probability theories with both classical and contemporary IT applications. Each concept is reinforced with tightly-coupled exercise sets, and the associated fundamentals are explored mostly from first principles. Furthermore, it includes programming implementations of illustrative examples and algorithms, complemented by a brief Python tutorial. Departing from traditional organization, the book adopts a lecture-notes format, presenting interconnected themes and storylines. Primarily tailored for sophomore-level undergraduates, it also suits junior and senior-level courses. While readers benefit from mathematical maturity and programming exposure, supplementary materials and exercise problems aid understanding. Part III serves to inspire and provide insights for students and professionals alike, underscoring the pragmatic relevance of probabilistic concepts in IT.
Probability for Kids: Using Model-Eliciting Activities to Investigate Probability Concepts (Grades 4-6)
by Scott ChamberlinProbability for Kids features real-world probability scenarios for students in grades 4-6. Students will encounter problems in which they read about students their age selling magazines for a school fund raiser, concerned about their homeroom assignments, and trying to decode the combination to a safe that their grandfather abandoned, among others, all of which maximizes learning so students gain a deep understanding of concepts in probability. This book will help teachers, parents, and other educators to employ best practices in implementing challenging math activities based on standards. Problem solvers who complete all six activities in the book will understand the six basic principles of probability and be high school ready for discussions in probability. Grades 4-6
Probability for Physicists
by Simon SircaThis book is designed as a practical and intuitive introduction to probability, statistics and random quantities for physicists. The book aims at getting to the main points by a clear, hands-on exposition supported by well-illustrated and worked-out examples. A strong focus on applications in physics and other natural sciences is maintained throughout. In addition to basic concepts of random variables, distributions, expected values and statistics, the book discusses the notions of entropy, Markov processes, and fundamentals of random number generation and Monte-Carlo methods.
Probability for Statisticians
by Galen R. ShorackThe choice of examples used in this text clearly illustrate its use for a one-year graduate course. The material to be presented in the classroom constitutes a little more than half the text, while the rest of the text provides background, offers different routes that could be pursued in the classroom, as well as additional material that is appropriate for self-study. Of particular interest is a presentation of the major central limit theorems via Steins method either prior to or alternative to a characteristic function presentation. Additionally, there is considerable emphasis placed on the quantile function as well as the distribution function, with both the bootstrap and trimming presented. The section on martingales covers censored data martingales.
Probability for Statistics and Machine Learning
by Anirban DasguptaThis book provides a versatile and lucid treatment of classic as well as modern probability theory, while integrating them with core topics in statistical theory and also some key tools in machine learning. It is written in an extremely accessible style, with elaborate motivating discussions and numerous worked out examples and exercises. The book has 20 chapters on a wide range of topics, 423 worked out examples, and 808 exercises. It is unique in its unification of probability and statistics, its coverage and its superb exercise sets, detailed bibliography, and in its substantive treatment of many topics of current importance. This book can be used as a text for a year long graduate course in statistics, computer science, or mathematics, for self-study, and as an invaluable research reference on probabiliity and its applications. Particularly worth mentioning are the treatments of distribution theory, asymptotics, simulation and Markov Chain Monte Carlo, Markov chains and martingales, Gaussian processes, VC theory, probability metrics, large deviations, bootstrap, the EM algorithm, confidence intervals, maximum likelihood and Bayes estimates, exponential families, kernels, and Hilbert spaces, and a self contained complete review of univariate probability.
Probability Foundations for Engineers
by Joel A. NachlasThis textbook will continue to be the best suitable textbook written specifically for a first course on probability theory and designed for industrial engineering and operations management students. The book offers theory in an accessible manner and includes numerous practical examples based on engineering applications. Probability Foundations for Engineers, Second Edition continues to focus specifically on probability rather than probability and statistics. It offers a conversational presentation rather than a theorem or proof and includes examples based on engineering applications as it highlights Excel computations. This new edition presents a review of set theory and updates all descriptions, such as events versus outcomes, so that they are more understandable. Additional new material includes distributions such as beta and lognormal, a section on counting principles for defining probabilities, a section on mixture distributions and a pair of distribution summary tables. Intended for undergraduate engineering students, this new edition textbook offers a foundational knowledge of probability. It is also useful to engineers already in the field who want to learn more about probability concepts. An updated solutions manual is available for qualified textbook adoptions.
Probability Foundations for Engineers
by Joel A. NachlasSuitable for a first course in probability theory, this textbook covers theory in an accessible manner and includes numerous practical examples based on engineering applications. The book begins with a summary of set theory and then introduces probability and its axioms. It covers conditional probability, independence, and approximations. An important aspect of the text is the fact that examples are not presented in terms of "balls in urns". Many examples do relate to gambling with coins, dice and cards but most are based on observable physical phenomena familiar to engineering students.
Probability in Complex Physical Systems
by Barbara Gentz Jean-Dominique Deuschel Max Von Renesse Michael Scheutzow Uwe Schmock Wolfgang KönigProbabilistic approaches have played a prominent role in the study of complex physical systems for more than thirty years. This volume collects twenty articles on various topics in this field, including self-interacting random walks and polymer models in random and non-random environments, branching processes, Parisi formulas and metastability in spin glasses, and hydrodynamic limits for gradient Gibbs models. The majority of these articles contain original results at the forefront of contemporary research; some of them include review aspects and summarize the state-of-the-art on topical issues - one focal point is the parabolic Anderson model, which is considered with various novel aspects including moving catalysts, acceleration and deceleration and fron propagation, for both time-dependent and time-independent potentials. The authors are among the world's leading experts. This Festschrift honours two eminent researchers, Erwin Bolthausen and Jürgen Gärtner, whose scientific work has profoundly influenced the field and all of the present contributions.
Probability in Electrical Engineering and Computer Science: An Application-Driven Course
by Jean WalrandThis revised textbook motivates and illustrates the techniques of applied probability by applications in electrical engineering and computer science (EECS). The author presents information processing and communication systems that use algorithms based on probabilistic models and techniques, including web searches, digital links, speech recognition, GPS, route planning, recommendation systems, classification, and estimation. He then explains how these applications work and, along the way, provides the readers with the understanding of the key concepts and methods of applied probability. Python labs enable the readers to experiment and consolidate their understanding. The book includes homework, solutions, and Jupyter notebooks. This edition includes new topics such as Boosting, Multi-armed bandits, statistical tests, social networks, queuing networks, and neural networks. For ancillaries related to this book, including examples of Python demos and also Python labs used in Berkeley, please email Mary James at mary.james@springer.com. This is an open access book.
Probability in Physics
by Meir Hemmo Yemima Ben-MenahemWhat is the role and meaning of probability in physical theory, in particular in two of the most successful theories of our age, quantum physics and statistical mechanics? Laws once conceived as universal and deterministic, such as Newton's laws of motion, or the second law of thermodynamics, are replaced in these theories by inherently probabilistic laws. This collection of essays by some of the world's foremost experts presents an in-depth analysis of the meaning of probability in contemporary physics. Among the questions addressed are: How are probabilities defined? Are they objective or subjective? What is their explanatory value? What are the differences between quantum and classical probabilities? The result is an informative and thought-provoking book for the scientifically inquisitive.
Probability in Physics: An Introductory Guide (Undergraduate Lecture Notes in Physics)
by Andy LawrenceThis textbook presents an introduction to the use of probability in physics, treating introductory ideas of both statistical physics and of statistical inference, as well the importance of probability in information theory, quantum mechanics, and stochastic processes, in a unified manner. The book also presents a harmonised view of frequentist and Bayesian approaches to inference, emphasising their complementary value. The aim is to steer a middle course between the "cookbook" style and an overly dry mathematical statistics style. The treatment is driven by real physics examples throughout, but developed with a level of mathematical clarity and rigour appropriate to mid-career physics undergraduates. Exercises and solutions are included.
The Probability Integral: Its Origin, Its Importance, and Its Calculation
by Paul J. NahinThis book tells the story of the probability integral, the approaches to analyzing it throughout history, and the many areas of science where it arises. The so-called probability integral, the integral over the real line of a Gaussian function, occurs ubiquitously in mathematics, physics, engineering and probability theory. Stubbornly resistant to the undergraduate toolkit for handling integrals, calculating its value and investigating its properties occupied such mathematical luminaries as De Moivre, Laplace, Poisson, and Liouville. This book introduces the probability integral, puts it into a historical context, and describes the different approaches throughout history to evaluate and analyze it. The author also takes entertaining diversions into areas of math, science, and engineering where the probability integral arises: as well as being indispensable to probability theory and statistics, it also shows up naturally in thermodynamics and signal processing. Designed to be accessible to anyone at the undergraduate level and above, this book will appeal to anyone interested in integration techniques, as well as historians of math, science, and statistics.
The Probability Map of the Universe: Essays on David Albert’s <i>Time and Chance</i>
by Barry Loewer, Brad Weslake, and Eric WinsbergPhilosophers debate the ideas and implications of one of the most important contemporary works in the philosophy of science, David Albert’s Time and Chance.In the twenty-odd years since its publication, David Albert’s Time and Chance has been recognized as one of the most significant contemporary contributions to the philosophy of science. Here, philosophers and physicists explore the implications of Albert’s arguments and debate his solutions to some of the most intractable problems in theoretical physics.Albert has attempted to make sense of the tension between our best scientific pictures of the fundamental physical structure of the world and our everyday empirical experience of that world. In particular, he is concerned with problems arising from causality and the direction of time: defying common sense, almost all our basic scientific ideas suggest that whatever can happen can just as naturally happen in reverse. Focusing on Newtonian mechanics, Albert provides a systematic account of the temporal irreversibility of the Second Law of Thermodynamics, of the asymmetries in our epistemic access to the past and the future, and of our conviction that by acting now we can affect the future but not the past. He also generalizes the Newtonian picture to the quantum-mechanical case and suggests a deep potential connection between the problem of the direction of time and the quantum-mechanical measurement problem.The essays included in The Probability Map of the Universe develop, explore, and critique this account, while Albert himself replies. The result is an insightful discussion of the foundations of statistical mechanics and its relation to cosmology, the direction of time, and the metaphysical nature of laws and objective probability.
Probability, Markov Chains, Queues, and Simulation: The Mathematical Basis of Performance Modeling
by William J. StewartProbability, Markov Chains, Queues, and Simulation provides a modern and authoritative treatment of the mathematical processes that underlie performance modeling. The detailed explanations of mathematical derivations and numerous illustrative examples make this textbook readily accessible to graduate and advanced undergraduate students taking courses in which stochastic processes play a fundamental role. The textbook is relevant to a wide variety of fields, including computer science, engineering, operations research, statistics, and mathematics.The textbook looks at the fundamentals of probability theory, from the basic concepts of set-based probability, through probability distributions, to bounds, limit theorems, and the laws of large numbers. Discrete and continuous-time Markov chains are analyzed from a theoretical and computational point of view. Topics include the Chapman-Kolmogorov equations; irreducibility; the potential, fundamental, and reachability matrices; random walk problems; reversibility; renewal processes; and the numerical computation of stationary and transient distributions. The M/M/1 queue and its extensions to more general birth-death processes are analyzed in detail, as are queues with phase-type arrival and service processes. The M/G/1 and G/M/1 queues are solved using embedded Markov chains; the busy period, residual service time, and priority scheduling are treated. Open and closed queueing networks are analyzed. The final part of the book addresses the mathematical basis of simulation.Each chapter of the textbook concludes with an extensive set of exercises. An instructor's solution manual, in which all exercises are completely worked out, is also available (to professors only).Numerous examples illuminate the mathematical theoriesCarefully detailed explanations of mathematical derivations guarantee a valuable pedagogical approachEach chapter concludes with an extensive set of exercises
Probability Models
by John HaighThe purpose of this book is to provide a sound introduction to the study of real-world phenomena that possess random variation. It describes how to set up and analyse models of real-life phenomena that involve elements of chance. Motivation comes from everyday experiences of probability, such as that of a dice or cards, the idea of fairness in games of chance, and the random ways in which, say, birthdays are shared or particular events arise. Applications include branching processes, random walks, Markov chains, queues, renewal theory, and Brownian motion. This popular second edition textbook contains many worked examples and several chapters have been updated and expanded. Some mathematical knowledge is assumed. The reader should have the ability to work with unions, intersections and complements of sets; a good facility with calculus, including integration, sequences and series; and appreciation of the logical development of an argument. Probability Models is designed to aid students studying probability as part of an undergraduate course on mathematics or mathematics and statistics.
Probability Models for Economic Decisions (The MIT Press)
by Roger B. Myerson Eduardo ZambranoAn introduction to the use of probability models for analyzing risk and economic decisions, using spreadsheets to represent and simulate uncertainty.This textbook offers an introduction to the use of probability models for analyzing risks and economic decisions. It takes a learn-by-doing approach, teaching the student to use spreadsheets to represent and simulate uncertainty and to analyze the effect of such uncertainty on an economic decision. Students in applied business and economics can more easily grasp difficult analytical methods with Excel spreadsheets. The book covers the basic ideas of probability, how to simulate random variables, and how to compute conditional probabilities via Monte Carlo simulation. The first four chapters use a large collection of probability distributions to simulate a range of problems involving worker efficiency, market entry, oil exploration, repeated investment, and subjective belief elicitation. The book then covers correlation and multivariate normal random variables; conditional expectation; optimization of decision variables, with discussions of the strategic value of information, decision trees, game theory, and adverse selection; risk sharing and finance; dynamic models of growth; dynamic models of arrivals; and model risk. New material in this second edition includes two new chapters on additional dynamic models and model risk; new sections in every chapter; many new end-of-chapter exercises; and coverage of such topics as simulation model workflow, models of probabilistic electoral forecasting, and real options. The book comes equipped with Simtools, an open-source, free software used througout the book, which allows students to conduct Monte Carlo simulations seamlessly in Excel.
Probability Models for Economic Decisions, second edition (The\mit Press Ser.)
by Roger B. Myerson Eduardo ZambranoAn introduction to the use of probability models for analyzing risk and economic decisions, using spreadsheets to represent and simulate uncertainty.This textbook offers an introduction to the use of probability models for analyzing risks and economic decisions. It takes a learn-by-doing approach, teaching the student to use spreadsheets to represent and simulate uncertainty and to analyze the effect of such uncertainty on an economic decision. Students in applied business and economics can more easily grasp difficult analytical methods with Excel spreadsheets. The book covers the basic ideas of probability, how to simulate random variables, and how to compute conditional probabilities via Monte Carlo simulation. The first four chapters use a large collection of probability distributions to simulate a range of problems involving worker efficiency, market entry, oil exploration, repeated investment, and subjective belief elicitation. The book then covers correlation and multivariate normal random variables; conditional expectation; optimization of decision variables, with discussions of the strategic value of information, decision trees, game theory, and adverse selection; risk sharing and finance; dynamic models of growth; dynamic models of arrivals; and model risk. New material in this second edition includes two new chapters on additional dynamic models and model risk; new sections in every chapter; many new end-of-chapter exercises; and coverage of such topics as simulation model workflow, models of probabilistic electoral forecasting, and real options. The book comes equipped with Simtools, an open-source, free software used througout the book, which allows students to conduct Monte Carlo simulations seamlessly in Excel.
Probability Models in Operations Research (Operations Research Series)
by C. Richard Cassady Joel A. NachlasIndustrial engineering has expanded from its origins in manufacturing to transportation, health care, logistics, services, and more. A common denominator among all these industries, and one of the biggest challenges facing decision-makers, is the unpredictability of systems. Probability Models in Operations Research provides a comprehensive
The Probability of God: A Simple Calculation That Proves the Ultimate Truth
by Dr. Stephen D. UnwinDoes God exist?This is probably the most debated question in the history of mankind. Scholars, scientists, and philosophers have spent their lifetimes trying to prove or disprove the existence of God, only to have their theories crucified by other scholars, scientists, and philosophers. Where the debate breaks down is in the ambiguities and colloquialisms of language. But, by using a universal, unambiguous language—namely, mathematics—can this question finally be answered definitively? That’s what Dr. Stephen Unwin attempts to do in this riveting, accessible, and witty book, The Probability of God.At its core, this groundbreaking book reveals how a math equation developed more than 200 years ago by noted European philosopher Thomas Bayes can be used to calculate the probability that God exists. The equation itself is much more complicated than a simple coin toss (heads, He’s up there running the show; tails, He’s not). Yet Dr. Unwin writes with a clarity that makes his mathematical proof easy for even the nonmathematician to understand and a verve that makes his book a delight to read. Leading you carefully through each step in his argument, he demonstrates in the end that God does indeed exist.Whether you’re a devout believer and agree with Dr. Unwin’s proof or are unsure about all things divine, you will find this provocative book enlightening and engaging.
Probability on Compact Lie Groups
by David ApplebaumProbability theory on compact Lie groups deals with the interaction between "chance" and "symmetry," a beautiful area of mathematics of great interest in its own sake but which is now also finding increasing applications in statistics and engineering (particularly with respect to signal processing). The author gives a comprehensive introduction to some of the principle areas of study, with an emphasis on applicability. The most important topics presented are: the study of measures via the non-commutative Fourier transform, existence and regularity of densities, properties of random walks and convolution semigroups of measures and the statistical problem of deconvolution. The emphasis on compact (rather than general) Lie groups helps readers to get acquainted with what is widely seen as a difficult field but which is also justified by the wealth of interesting results at this level and the importance of these groups for applications. The book is primarily aimed at researchers working in probability, stochastic analysis and harmonic analysis on groups. It will also be of interest to mathematicians working in Lie theory and physicists, statisticians and engineers who are working on related applications. A background in first year graduate level measure theoretic probability and functional analysis is essential; a background in Lie groups and representation theory is certainly helpful but the first two chapters also offer orientation in these subjects.
Probability on Graphs: Random Processes on Graphs and Lattices (Institute of Mathematical Statistics Textbooks #8)
by Geoffrey GrimmettThis introduction to some of the principal models in the theory of disordered systems leads the reader through the basics, to the very edge of contemporary research, with the minimum of technical fuss. Topics covered include random walk, percolation, self-avoiding walk, interacting particle systems, uniform spanning tree, random graphs, as well as the Ising, Potts, and random-cluster models for ferromagnetism, and the Lorentz model for motion in a random medium. Schramm-Lwner evolutions (SLE) arise in various contexts. The choice of topics is strongly motivated by modern applications and focuses on areas that merit further research. Special features include a simple account of Smirnov's proof of Cardy's formula for critical percolation, and a fairly full account of the theory of influence and sharp-thresholds. Accessible to a wide audience of mathematicians and physicists, this book can be used as a graduate course text. Each chapter ends with a range of exercises.
Probability on Graphs
by Geoffrey GrimmettThis introduction to some of the principal models in the theory of disordered systems leads the reader through the basics, to the very edge of contemporary research, with the minimum of technical fuss. Topics covered include random walk, percolation, self-avoiding walk, interacting particle systems, uniform spanning tree, random graphs, as well as the Ising, Potts, and random-cluster models for ferromagnetism, and the Lorentz model for motion in a random medium. Schramm-Löwner evolutions (SLE) arise in various contexts. The choice of topics is strongly motivated by modern applications and focuses on areas that merit further research. Special features include a simple account of Smirnov's proof of Cardy's formula for critical percolation, and a fairly full account of the theory of influence and sharp-thresholds. Accessible to a wide audience of mathematicians and physicists, this book can be used as a graduate course text. Each chapter ends with a range of exercises.
Probability on Real Lie Algebras
by Uwe Franz Nicolas PrivaultThis monograph is a progressive introduction to non-commutativity in probability theory, summarizing and synthesizing recent results about classical and quantum stochastic processes on Lie algebras. In the early chapters, focus is placed on concrete examples of the links between algebraic relations and the moments of probability distributions. The subsequent chapters are more advanced and deal with Wigner densities for non-commutative couples of random variables, non-commutative stochastic processes with independent increments (quantum Lévy processes), and the quantum Malliavin calculus. This book will appeal to advanced undergraduate and graduate students interested in the relations between algebra, probability, and quantum theory. It also addresses a more advanced audience by covering other topics related to non-commutativity in stochastic calculus, Lévy processes, and the Malliavin calculus.
Probability, Random Processes, and Statistical Analysis
by Hisashi Kobayashi Brian L. Mark William TurinTogether with the fundamentals of probability, random processes, and statistical analysis, this insightful book also presents a broad range of advanced topics and applications. There is extensive coverage of Bayesian vs. frequentist statistics, time series and spectral representation, inequalities, bound and approximation, maximum-likelihood estimation and the expectation-maximization (EM) algorithm, geometric Brownian motion and Itô process. Applications such as hidden Markov models (HMM), the Viterbi, BCJR, and Baum-Welch algorithms, algorithms for machine learning, Wiener and Kalman filters, queueing and loss networks, and are treated in detail. The book will be useful to students and researchers in such areas as communications, signal processing, networks, machine learning, bioinformatics, econometrics and mathematical finance. With a solutions manual, lecture slides, supplementary materials, and MATLAB programs all available online, it is ideal for classroom teaching as well as a valuable reference for professionals.