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Author: J. Hoffman-Jorgensen
Publisher: Routledge
ISBN: 1351421549
Category : Mathematics
Languages : en
Pages : 296
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Book Description
Volume II of this two-volume text and reference work concentrates on the applications of probability theory to statistics, e.g., the art of calculating densities of complicated transformations of random vectors, exponential models, consistency of maximum estimators, and asymptotic normality of maximum estimators. It also discusses topics of a pure probabilistic nature, such as stochastic processes, regular conditional probabilities, strong Markov chains, random walks, and optimal stopping strategies in random games. Unusual topics include the transformation theory of densities using Hausdorff measures, the consistency theory using the upper definition function, and the asymptotic normality of maximum estimators using twice stochastic differentiability. With an emphasis on applications to statistics, this is a continuation of the first volume, though it may be used independently of that book. Assuming a knowledge of linear algebra and analysis, as well as a course in modern probability, Volume II looks at statistics from a probabilistic point of view, touching only slightly on the practical computation aspects.
Author: J. Hoffman-Jorgensen
Publisher: Routledge
ISBN: 1351421549
Category : Mathematics
Languages : en
Pages : 296
Get Book
Book Description
Volume II of this two-volume text and reference work concentrates on the applications of probability theory to statistics, e.g., the art of calculating densities of complicated transformations of random vectors, exponential models, consistency of maximum estimators, and asymptotic normality of maximum estimators. It also discusses topics of a pure probabilistic nature, such as stochastic processes, regular conditional probabilities, strong Markov chains, random walks, and optimal stopping strategies in random games. Unusual topics include the transformation theory of densities using Hausdorff measures, the consistency theory using the upper definition function, and the asymptotic normality of maximum estimators using twice stochastic differentiability. With an emphasis on applications to statistics, this is a continuation of the first volume, though it may be used independently of that book. Assuming a knowledge of linear algebra and analysis, as well as a course in modern probability, Volume II looks at statistics from a probabilistic point of view, touching only slightly on the practical computation aspects.
Author: J. Hoffman-Jorgensen
Publisher: Routledge
ISBN: 1351421581
Category : Mathematics
Languages : en
Pages : 630
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Book Description
Volume I of this two-volume text and reference work begins by providing a foundation in measure and integration theory. It then offers a systematic introduction to probability theory, and in particular, those parts that are used in statistics. This volume discusses the law of large numbers for independent and non-independent random variables, transforms, special distributions, convergence in law, the central limit theorem for normal and infinitely divisible laws, conditional expectations and martingales. Unusual topics include the uniqueness and convergence theorem for general transforms with characteristic functions, Laplace transforms, moment transforms and generating functions as special examples. The text contains substantive applications, e.g., epidemic models, the ballot problem, stock market models and water reservoir models, and discussion of the historical background. The exercise sets contain a variety of problems ranging from simple exercises to extensions of the theory.
Author: Bruno de Finetti
Publisher: John Wiley & Sons
ISBN: 1119286379
Category : Mathematics
Languages : en
Pages : 611
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Book Description
First issued in translation as a two-volume work in 1975, this classic book provides the first complete development of the theory of probability from a subjectivist viewpoint. It proceeds from a detailed discussion of the philosophical mathematical aspects to a detailed mathematical treatment of probability and statistics. De Finetti's theory of probability is one of the foundations of Bayesian theory. De Finetti stated that probability is nothing but a subjective analysis of the likelihood that something will happen and that that probability does not exist outside the mind. It is the rate at which a person is willing to bet on something happening. This view is directly opposed to the classicist/ frequentist view of the likelihood of a particular outcome of an event, which assumes that the same event could be identically repeated many times over, and the 'probability' of a particular outcome has to do with the fraction of the time that outcome results from the repeated trials.
Author: Roman Vershynin
Publisher: Cambridge University Press
ISBN: 1108415199
Category : Business & Economics
Languages : en
Pages : 299
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Book Description
An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.
Author: Jørgen Hoffmann-Jørgensen
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: J. Hoffman-Jorgensen
Publisher: CRC Press
ISBN: 9780412052316
Category : Mathematics
Languages : en
Pages : 554
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Book Description
Volume II of this two-volume text and reference work concentrates on the applications of probability theory to statistics, e.g., the art of calculating densities of complicated transformations of random vectors, exponential models, consistency of maximum estimators, and asymptotic normality of maximum estimators. It also discusses topics of a pure probabilistic nature, such as stochastic processes, regular conditional probabilities, strong Markov chains, random walks, and optimal stopping strategies in random games. Unusual topics include the transformation theory of densities using Hausdorff measures, the consistency theory using the upper definition function, and the asymptotic normality of maximum estimators using twice stochastic differentiability. With an emphasis on applications to statistics, this is a continuation of the first volume, though it may be used independently of that book. Assuming a knowledge of linear algebra and analysis, as well as a course in modern probability, Volume II looks at statistics from a probabilistic point of view, touching only slightly on the practical computation aspects.
Author: David F. Anderson
Publisher: Cambridge University Press
ISBN: 110824498X
Category : Mathematics
Languages : en
Pages : 447
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Book Description
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: Daniel W. Stroock
Publisher: Cambridge University Press
ISBN: 1139494619
Category : Mathematics
Languages : en
Pages : 550
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Book Description
This second edition of Daniel W. Stroock's text is suitable for first-year graduate students with a good grasp of introductory, undergraduate probability theory and a sound grounding in analysis. It is intended to provide readers with an introduction to probability theory and the analytic ideas and tools on which the modern theory relies. It includes more than 750 exercises. Much of the content has undergone significant revision. In particular, the treatment of Levy processes has been rewritten, and a detailed account of Gaussian measures on a Banach space is given.
Author: F.M. Dekking
Publisher: Springer Science & Business Media
ISBN: 1846281687
Category : Mathematics
Languages : en
Pages : 488
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Book Description
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
Author: J. Hoffman-Jorgensen
Publisher: Routledge
ISBN: 1351421557
Category : Mathematics
Languages : en
Pages : 552
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Book Description
Volume II of this two-volume text and reference work concentrates on the applications of probability theory to statistics, e.g., the art of calculating densities of complicated transformations of random vectors, exponential models, consistency of maximum estimators, and asymptotic normality of maximum estimators. It also discusses topics of a pure probabilistic nature, such as stochastic processes, regular conditional probabilities, strong Markov chains, random walks, and optimal stopping strategies in random games. Unusual topics include the transformation theory of densities using Hausdorff measures, the consistency theory using the upper definition function, and the asymptotic normality of maximum estimators using twice stochastic differentiability. With an emphasis on applications to statistics, this is a continuation of the first volume, though it may be used independently of that book. Assuming a knowledge of linear algebra and analysis, as well as a course in modern probability, Volume II looks at statistics from a probabilistic point of view, touching only slightly on the practical computation aspects.
