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| Author | : David Temperley |
| Publisher | : MIT Press |
| Total Pages | : 257 |
| Release | : 2007 |
| Genre | : Mathematics |
| ISBN | : 0262201666 |
Exploring the application of Bayesian probabilistic modeling techniques to musical issues, including the perception of key and meter.
| Author | : David Temperley |
| Publisher | : MIT Press |
| Total Pages | : 432 |
| Release | : 2004-08-20 |
| Genre | : Music |
| ISBN | : 9780262701051 |
In this book, David Temperley addresses a fundamental question about music cognition: how do we extract basic kinds of musical information, such as meter, phrase structure, counterpoint, pitch spelling, harmony, and key from music as we hear it? Taking a computational approach, Temperley develops models for generating these aspects of musical structure. The models he proposes are based on preference rules, which are criteria for evaluating a possible structural analysis of a piece of music. A preference rule system evaluates many possible interpretations and chooses the one that best satisfies the rules. After an introductory chapter, Temperley presents preference rule systems for generating six basic kinds of musical structure: meter, phrase structure, contrapuntal structure, harmony, and key, as well as pitch spelling (the labeling of pitch events with spellings such as A flat or G sharp). He suggests that preference rule systems not only show how musical structures are inferred, but also shed light on other aspects of music. He substantiates this claim with discussions of musical ambiguity, retrospective revision, expectation, and music outside the Western canon (rock and traditional African music). He proposes a framework for the description of musical styles based on preference rule systems and explores the relevance of preference rule systems to higher-level aspects of music, such as musical schemata, narrative and drama, and musical tension.
| Author | : David F. Anderson |
| Publisher | : Cambridge University Press |
| Total Pages | : 447 |
| Release | : 2017-11-02 |
| Genre | : Mathematics |
| ISBN | : 110824498X |
This classroom-tested textbook is an introduction to probability theory, with the right balance between mathematical precision, probabilistic intuition, and concrete applications. Introduction to Probability covers the material precisely, while avoiding excessive technical details. After introducing the basic vocabulary of randomness, including events, probabilities, and random variables, the text offers the reader a first glimpse of the major theorems of the subject: the law of large numbers and the central limit theorem. The important probability distributions are introduced organically as they arise from applications. The discrete and continuous sides of probability are treated together to emphasize their similarities. Intended for students with a calculus background, the text teaches not only the nuts and bolts of probability theory and how to solve specific problems, but also why the methods of solution work.
| Author | : John E. Freund |
| Publisher | : Courier Corporation |
| Total Pages | : 276 |
| Release | : 2012-05-11 |
| Genre | : Mathematics |
| ISBN | : 0486158438 |
Featured topics include permutations and factorials, probabilities and odds, frequency interpretation, mathematical expectation, decision making, postulates of probability, rule of elimination, much more. Exercises with some solutions. Summary. 1973 edition.
| Author | : Narayanaswamy Balakrishnan |
| Publisher | : John Wiley & Sons |
| Total Pages | : 548 |
| Release | : 2021-11-24 |
| Genre | : Mathematics |
| ISBN | : 1118548558 |
INTRODUCTION TO PROBABILITY Discover practical models and real-world applications of multivariate models useful in engineering, business, and related disciplines In Introduction to Probability: Multivariate Models and Applications, a team of distinguished researchers delivers a comprehensive exploration of the concepts, methods, and results in multivariate distributions and models. Intended for use in a second course in probability, the material is largely self-contained, with some knowledge of basic probability theory and univariate distributions as the only prerequisite. This textbook is intended as the sequel to Introduction to Probability: Models and Applications. Each chapter begins with a brief historical account of some of the pioneers in probability who made significant contributions to the field. It goes on to describe and explain a critical concept or method in multivariate models and closes with two collections of exercises designed to test basic and advanced understanding of the theory. A wide range of topics are covered, including joint distributions for two or more random variables, independence of two or more variables, transformations of variables, covariance and correlation, a presentation of the most important multivariate distributions, generating functions and limit theorems. This important text: Includes classroom-tested problems and solutions to probability exercises Highlights real-world exercises designed to make clear the concepts presented Uses Mathematica software to illustrate the text’s computer exercises Features applications representing worldwide situations and processes Offers two types of self-assessment exercises at the end of each chapter, so that students may review the material in that chapter and monitor their progress Perfect for students majoring in statistics, engineering, business, psychology, operations research and mathematics taking a second course in probability, Introduction to Probability: Multivariate Models and Applications is also an indispensable resource for anyone who is required to use multivariate distributions to model the uncertainty associated with random phenomena.
| Author | : Ruma Falk |
| Publisher | : A K Peters/CRC Press |
| Total Pages | : 264 |
| Release | : 1993-04-15 |
| Genre | : Mathematics |
| ISBN | : |
| Author | : T. T. Soong |
| Publisher | : John Wiley & Sons |
| Total Pages | : 406 |
| Release | : 2004-06-25 |
| Genre | : Mathematics |
| ISBN | : 0470868155 |
This textbook differs from others in the field in that it has been prepared very much with students and their needs in mind, having been classroom tested over many years. It is a true “learner’s book” made for students who require a deeper understanding of probability and statistics. It presents the fundamentals of the subject along with concepts of probabilistic modelling, and the process of model selection, verification and analysis. Furthermore, the inclusion of more than 100 examples and 200 exercises (carefully selected from a wide range of topics), along with a solutions manual for instructors, means that this text is of real value to students and lecturers across a range of engineering disciplines. Key features: Presents the fundamentals in probability and statistics along with relevant applications. Explains the concept of probabilistic modelling and the process of model selection, verification and analysis. Definitions and theorems are carefully stated and topics rigorously treated. Includes a chapter on regression analysis. Covers design of experiments. Demonstrates practical problem solving throughout the book with numerous examples and exercises purposely selected from a variety of engineering fields. Includes an accompanying online Solutions Manual for instructors containing complete step-by-step solutions to all problems.
| Author | : Joseph K. Blitzstein |
| Publisher | : CRC Press |
| Total Pages | : 599 |
| Release | : 2014-07-24 |
| Genre | : Mathematics |
| ISBN | : 1466575573 |
Developed from celebrated Harvard statistics lectures, Introduction to Probability provides essential language and tools for understanding statistics, randomness, and uncertainty. The book explores a wide variety of applications and examples, ranging from coincidences and paradoxes to Google PageRank and Markov chain Monte Carlo (MCMC). Additional application areas explored include genetics, medicine, computer science, and information theory. The print book version includes a code that provides free access to an eBook version. The authors present the material in an accessible style and motivate concepts using real-world examples. Throughout, they use stories to uncover connections between the fundamental distributions in statistics and conditioning to reduce complicated problems to manageable pieces. The book includes many intuitive explanations, diagrams, and practice problems. Each chapter ends with a section showing how to perform relevant simulations and calculations in R, a free statistical software environment.
| Author | : Alfred Renyi |
| Publisher | : Courier Corporation |
| Total Pages | : 386 |
| Release | : 2007-01-01 |
| Genre | : Mathematics |
| ISBN | : 0486462617 |
Introducing many innovations in content and methods, this book involves the foundations, basic concepts, and fundamental results of probability theory. Geared toward readers seeking a firm basis for study of mathematical statistics or information theory, it also covers the mathematical notions of experiments and independence. 1970 edition.
| Author | : Boris Vladimirovich Gnedenko |
| Publisher | : Courier Corporation |
| Total Pages | : 162 |
| Release | : 1962-01-01 |
| Genre | : Mathematics |
| ISBN | : 0486601552 |
This compact volume equips the reader with all the facts and principles essential to a fundamental understanding of the theory of probability. It is an introduction, no more: throughout the book the authors discuss the theory of probability for situations having only a finite number of possibilities, and the mathematics employed is held to the elementary level. But within its purposely restricted range it is extremely thorough, well organized, and absolutely authoritative. It is the only English translation of the latest revised Russian edition; and it is the only current translation on the market that has been checked and approved by Gnedenko himself. After explaining in simple terms the meaning of the concept of probability and the means by which an event is declared to be in practice, impossible, the authors take up the processes involved in the calculation of probabilities. They survey the rules for addition and multiplication of probabilities, the concept of conditional probability, the formula for total probability, Bayes's formula, Bernoulli's scheme and theorem, the concepts of random variables, insufficiency of the mean value for the characterization of a random variable, methods of measuring the variance of a random variable, theorems on the standard deviation, the Chebyshev inequality, normal laws of distribution, distribution curves, properties of normal distribution curves, and related topics. The book is unique in that, while there are several high school and college textbooks available on this subject, there is no other popular treatment for the layman that contains quite the same material presented with the same degree of clarity and authenticity. Anyone who desires a fundamental grasp of this increasingly important subject cannot do better than to start with this book. New preface for Dover edition by B. V. Gnedenko.
