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Probability for Statisticians

Probability for Statisticians
Author: Galen R. Shorack
Publisher: Springer
Total Pages: 519
Release: 2017-09-21
Genre: Mathematics
ISBN: 3319522078

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The 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.


Essentials of Probability Theory for Statisticians

Essentials of Probability Theory for Statisticians
Author: Michael A. Proschan
Publisher: CRC Press
Total Pages: 334
Release: 2016-03-23
Genre: Mathematics
ISBN: 1498704204

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Essentials of Probability Theory for Statisticians provides graduate students with a rigorous treatment of probability theory, with an emphasis on results central to theoretical statistics. It presents classical probability theory motivated with illustrative examples in biostatistics, such as outlier tests, monitoring clinical trials, and using adaptive methods to make design changes based on accumulating data. The authors explain different methods of proofs and show how they are useful for establishing classic probability results. After building a foundation in probability, the text intersperses examples that make seemingly esoteric mathematical constructs more intuitive. These examples elucidate essential elements in definitions and conditions in theorems. In addition, counterexamples further clarify nuances in meaning and expose common fallacies in logic. This text encourages students in statistics and biostatistics to think carefully about probability. It gives them the rigorous foundation necessary to provide valid proofs and avoid paradoxes and nonsensical conclusions.


Probability, Statistics, and Truth

Probability, Statistics, and Truth
Author: Richard Von Mises
Publisher: Courier Corporation
Total Pages: 273
Release: 1981-01-01
Genre: Mathematics
ISBN: 0486242145

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This comprehensive study of probability considers the approaches of Pascal, Laplace, Poisson, and others. It also discusses Laws of Large Numbers, the theory of errors, and other relevant topics.


A Modern Introduction to Probability and Statistics

A Modern Introduction to Probability and Statistics
Author: F.M. Dekking
Publisher: Springer Science & Business Media
Total Pages: 485
Release: 2006-03-30
Genre: Mathematics
ISBN: 1846281687

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Suitable for self study Use real examples and real data sets that will be familiar to the audience Introduction to the bootstrap is included – this is a modern method missing in many other books


Probability and Statistics

Probability and Statistics
Author: Michael J. Evans
Publisher: Macmillan
Total Pages: 704
Release: 2004
Genre: Mathematics
ISBN: 9780716747420

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Unlike traditional introductory math/stat textbooks, Probability and Statistics: The Science of Uncertainty brings a modern flavor based on incorporating the computer to the course and an integrated approach to inference. From the start the book integrates simulations into its theoretical coverage, and emphasizes the use of computer-powered computation throughout.* Math and science majors with just one year of calculus can use this text and experience a refreshing blend of applications and theory that goes beyond merely mastering the technicalities. They'll get a thorough grounding in probability theory, and go beyond that to the theory of statistical inference and its applications. An integrated approach to inference is presented that includes the frequency approach as well as Bayesian methodology. Bayesian inference is developed as a logical extension of likelihood methods. A separate chapter is devoted to the important topic of model checking and this is applied in the context of the standard applied statistical techniques. Examples of data analyses using real-world data are presented throughout the text. A final chapter introduces a number of the most important stochastic process models using elementary methods. *Note: An appendix in the book contains Minitab code for more involved computations. The code can be used by students as templates for their own calculations. If a software package like Minitab is used with the course then no programming is required by the students.


Probability for Statisticians

Probability for Statisticians
Author: Galen R. Shorack
Publisher: Springer Science & Business Media
Total Pages: 599
Release: 2006-05-02
Genre: Mathematics
ISBN: 0387227601

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The 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 and Statistics

Probability and Statistics
Author: Ronald Deep
Publisher: Elsevier
Total Pages: 707
Release: 2005-10-25
Genre: Mathematics
ISBN: 0080480381

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Probability and Statistics is a calculus-based treatment of probability concurrent with and integrated with statistics. * Incorporates more than 1,000 engaging problems with answers* Includes more than 300 solved examples* Uses varied problem solving methods


Elements of Probability and Statistics

Elements of Probability and Statistics
Author: Francesca Biagini
Publisher: Springer
Total Pages: 246
Release: 2016-01-22
Genre: Mathematics
ISBN: 3319072544

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This book provides an introduction to elementary probability and to Bayesian statistics using de Finetti's subjectivist approach. One of the features of this approach is that it does not require the introduction of sample space – a non-intrinsic concept that makes the treatment of elementary probability unnecessarily complicate – but introduces as fundamental the concept of random numbers directly related to their interpretation in applications. Events become a particular case of random numbers and probability a particular case of expectation when it is applied to events. The subjective evaluation of expectation and of conditional expectation is based on an economic choice of an acceptable bet or penalty. The properties of expectation and conditional expectation are derived by applying a coherence criterion that the evaluation has to follow. The book is suitable for all introductory courses in probability and statistics for students in Mathematics, Informatics, Engineering, and Physics.


Probability and Statistics for Economists

Probability and Statistics for Economists
Author: Bruce Hansen
Publisher: Princeton University Press
Total Pages: 417
Release: 2022-06-28
Genre: Business & Economics
ISBN: 0691236143

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A comprehensive and up-to-date introduction to the mathematics that all economics students need to know Probability theory is the quantitative language used to handle uncertainty and is the foundation of modern statistics. Probability and Statistics for Economists provides graduate and PhD students with an essential introduction to mathematical probability and statistical theory, which are the basis of the methods used in econometrics. This incisive textbook teaches fundamental concepts, emphasizes modern, real-world applications, and gives students an intuitive understanding of the mathematics that every economist needs to know. Covers probability and statistics with mathematical rigor while emphasizing intuitive explanations that are accessible to economics students of all backgrounds Discusses random variables, parametric and multivariate distributions, sampling, the law of large numbers, central limit theory, maximum likelihood estimation, numerical optimization, hypothesis testing, and more Features hundreds of exercises that enable students to learn by doing Includes an in-depth appendix summarizing important mathematical results as well as a wealth of real-world examples Can serve as a core textbook for a first-semester PhD course in econometrics and as a companion book to Bruce E. Hansen’s Econometrics Also an invaluable reference for researchers and practitioners