Elements of Distribution Theory

Author: Thomas A. Severini

Publisher: Cambridge University Press

ISBN: 1139446118

Category: Mathematics

Page: N.A

View: 1520

This detailed introduction to distribution theory uses no measure theory, making it suitable for students in statistics and econometrics as well as for researchers who use statistical methods. Good backgrounds in calculus and linear algebra are important and a course in elementary mathematical analysis is useful, but not required. An appendix gives a detailed summary of the mathematical definitions and results that are used in the book. Topics covered range from the basic distribution and density functions, expectation, conditioning, characteristic functions, cumulants, convergence in distribution and the central limit theorem to more advanced concepts such as exchangeability, models with a group structure, asymptotic approximations to integrals, orthogonal polynomials and saddlepoint approximations. The emphasis is on topics useful in understanding statistical methodology; thus, parametric statistical models and the distribution theory associated with the normal distribution are covered comprehensively.

Brownian Motion

Author: Peter Mörters,Yuval Peres

Publisher: Cambridge University Press

ISBN: 1139486578

Category: Mathematics

Page: N.A

View: 7813

This eagerly awaited textbook covers everything the graduate student in probability wants to know about Brownian motion, as well as the latest research in the area. Starting with the construction of Brownian motion, the book then proceeds to sample path properties like continuity and nowhere differentiability. Notions of fractal dimension are introduced early and are used throughout the book to describe fine properties of Brownian paths. The relation of Brownian motion and random walk is explored from several viewpoints, including a development of the theory of Brownian local times from random walk embeddings. Stochastic integration is introduced as a tool and an accessible treatment of the potential theory of Brownian motion clears the path for an extensive treatment of intersections of Brownian paths. An investigation of exceptional points on the Brownian path and an appendix on SLE processes, by Oded Schramm and Wendelin Werner, lead directly to recent research themes.

Bayesian Nonparametrics

Author: Nils Lid Hjort,Chris Holmes,Peter Müller,Stephen G. Walker

Publisher: Cambridge University Press

ISBN: 1139484605

Category: Mathematics

Page: N.A

View: 4665

Bayesian nonparametrics works - theoretically, computationally. The theory provides highly flexible models whose complexity grows appropriately with the amount of data. Computational issues, though challenging, are no longer intractable. All that is needed is an entry point: this intelligent book is the perfect guide to what can seem a forbidding landscape. Tutorial chapters by Ghosal, Lijoi and Prünster, Teh and Jordan, and Dunson advance from theory, to basic models and hierarchical modeling, to applications and implementation, particularly in computer science and biostatistics. These are complemented by companion chapters by the editors and Griffin and Quintana, providing additional models, examining computational issues, identifying future growth areas, and giving links to related topics. This coherent text gives ready access both to underlying principles and to state-of-the-art practice. Specific examples are drawn from information retrieval, NLP, machine vision, computational biology, biostatistics, and bioinformatics.

Mathematical Reviews

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 3074

Confidence, Likelihood, Probability

Author: Tore Schweder,Nils Lid Hjort

Publisher: Cambridge University Press

ISBN: 0521861608

Category: Business & Economics

Page: 544

View: 2430

This is the first book to develop a methodology of confidence distributions, with a lively mix of theory, illustrations, applications and exercises.

Statistical Models

Author: A. C. Davison

Publisher: Cambridge University Press

ISBN: 9781139437417

Category: Mathematics

Page: N.A

View: 2827

Models and likelihood are the backbone of modern statistics. This 2003 book gives an integrated development of these topics that blends theory and practice, intended for advanced undergraduate and graduate students, researchers and practitioners. Its breadth is unrivaled, with sections on survival analysis, missing data, Markov chains, Markov random fields, point processes, graphical models, simulation and Markov chain Monte Carlo, estimating functions, asymptotic approximations, local likelihood and spline regressions as well as on more standard topics such as likelihood and linear and generalized linear models. Each chapter contains a wide range of problems and exercises. Practicals in the S language designed to build computing and data analysis skills, and a library of data sets to accompany the book, are available over the Web.

Probabilistic Methods in Combinatorial Analysis

Author: Vladimir Nikolaevich Sachkov

Publisher: Cambridge University Press

ISBN: 9780521455121

Category: Mathematics

Page: 246

View: 1852

This work explores the role of probabilistic methods for solving combinatorial problems. The subjects studied are nonnegative matrices, partitions and mappings of finite sets, with special emphasis on permutations and graphs, and equivalence classes specified on sequences of finite length consisting of elements of partially ordered sets; these define the probabilistic setting of Sachkov's general combinatorial scheme. The author pays special attention to using probabilistic methods to obtain asymptotic formulae that are difficult to derive using combinatorial methods. This important book describes many ideas not previously available in English and will be of interest to graduate students and professionals in mathematics and probability theory.

Probability with Martingales

Author: David Williams

Publisher: Cambridge University Press

ISBN: 9780521406055

Category: Mathematics

Page: 251

View: 9479

This is a masterly introduction to the modern and rigorous theory of probability. The author adopts the martingale theory as his main theme and moves at a lively pace through the subject's rigorous foundations. Measure theory is introduced and then immediately exploited by being applied to real probability theory. Classical results, such as Kolmogorov's Strong Law of Large Numbers and Three-Series Theorem are proved by martingale techniques. A proof of the Central Limit Theorem is also given. The author's style is entertaining and inimitable with pedagogy to the fore. Exercises play a vital role; there is a full quota of interesting and challenging problems, some with hints.

Probability Theory and Statistical Inference

Econometric Modeling with Observational Data

Author: Aris Spanos

Publisher: Cambridge University Press

ISBN: 9780521424080

Category: Business & Economics

Page: 815

View: 5708

A major textbook for students taking introductory courses in probability theory and statistical inference.

Cambridge Tracts in Mathematics

Author: Jean Bertoin

Publisher: Cambridge University Press

ISBN: 9780521646321

Category: Mathematics

Page: 266

View: 7270

This 1996 book is a comprehensive account of the theory of Lévy processes; aimed at probability theorists.

A Basic Course in Measure and Probability

Theory for Applications

Author: Ross Leadbetter,Stamatis Cambanis,Vladas Pipiras

Publisher: Cambridge University Press

ISBN: 1107020409

Category: Mathematics

Page: 376

View: 1135

A concise introduction covering all of the measure theory and probability most useful for statisticians.

Numerical Methods of Statistics

Author: John F. Monahan

Publisher: Cambridge University Press

ISBN: 9780521791687

Category: Computers

Page: 428

View: 3027

This 2001 book provides a basic background in numerical analysis and its applications in statistics.

Weak Convergence of Measures

Applications in Probability

Author: Patrick Billingsley

Publisher: SIAM

ISBN: 0898711762

Category: Mathematics

Page: 31

View: 3234

A treatment of the convergence of probability measures from the foundations to applications in limit theory for dependent random variables. Mapping theorems are proved via Skorokhod's representation theorem; Prokhorov's theorem is proved by construction of a content. The limit theorems at the conclusion are proved under a new set of conditions that apply fairly broadly, but at the same time make possible relatively simple proofs.

From Finite Sample to Asymptotic Methods in Statistics

Author: Pranab K. Sen,Julio M. Singer,Antonio C. Pedroso de Lima

Publisher: Cambridge University Press

ISBN: 0521877229

Category: Mathematics

Page: 386

View: 2282

A broad view of exact statistical inference and the development of asymptotic statistical inference.

Probabilistic Properties of Deterministic Systems

Author: Andrzej Lasota,Michael C. Mackey

Publisher: Cambridge University Press

ISBN: 9780521090964

Category: Mathematics

Page: 372

View: 8246

This book shows how densities arise in simple deterministic systems. There has been explosive growth in interest in physical, biological and economic systems that can be profitably studied using densities. Due to the inaccessibility of the mathematical literature there has been little diffusion of the applicable mathematics into the study of these 'chaotic' systems. This book will help to bridge that gap. The authors give a unified treatment of a variety of mathematical systems generating densities, ranging from one-dimensional discrete time transformations through continuous time systems described by integro-partial differential equations. They have drawn examples from many scientific fields to illustrate the utility of the techniques presented. The book assumes a knowledge of advanced calculus and differential equations, but basic concepts from measure theory, ergodic theory, the geometry of manifolds, partial differential equations, probability theory and Markov processes, and stochastic integrals and differential equations are introduced as needed.

The Theory of Probability

Explorations and Applications

Author: Santosh S. Venkatesh

Publisher: Cambridge University Press

ISBN: 1107024471

Category: Mathematics

Page: 805

View: 1578

From classical foundations to modern theory, this comprehensive guide to probability interweaves mathematical proofs, historical context and detailed illustrative applications.

Independent Random Variables and Rearrangement Invariant Spaces

Author: Michael Sh. Braverman,Mihail Šulevič Braverman

Publisher: Cambridge University Press

ISBN: 9780521455152

Category: Mathematics

Page: 115

View: 8347

Professor Braverman investigates independent random variables in rearrangement invariant (r.i.) spaces.

Foundations of Modern Probability

Author: Olav Kallenberg

Publisher: Springer Science & Business Media

ISBN: 0387227040

Category: Mathematics

Page: 523

View: 6199

Unique for its broad and yet comprehensive coverage of modern probability theory, ranging from first principles and standard textbook material to more advanced topics. In spite of the economical exposition, careful proofs are provided for all main results. After a detailed discussion of classical limit theorems, martingales, Markov chains, random walks, and stationary processes, the author moves on to a modern treatment of Brownian motion, L=82vy processes, weak convergence, It=93 calculus, Feller processes, and SDEs. The more advanced parts include material on local time, excursions, and additive functionals, diffusion processes, PDEs and potential theory, predictable processes, and general semimartingales. Though primarily intended as a general reference for researchers and graduate students in probability theory and related areas of analysis, the book is also suitable as a text for graduate and seminar courses on all levels, from elementary to advanced. Numerous easy to more challenging exercises are provided, especially for the early chapters. From the author of "Random Measures".