Download elements of distribution theory cambridge series in statistical and probabilistic mathematics in pdf or read elements of distribution theory cambridge series in statistical and probabilistic mathematics in pdf online books in PDF, EPUB and Mobi Format. Click Download or Read Online button to get elements of distribution theory cambridge series in statistical and probabilistic mathematics in pdf book now. This site is like a library, Use search box in the widget to get ebook that you want.



Elements Of Distribution Theory

Author: Thomas A. Severini
Publisher: Cambridge University Press
ISBN: 1139446118
Size: 16.76 MB
Format: PDF
View: 1363
Download and Read
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.

Confidence Likelihood Probability

Author: Tore Schweder
Publisher: Cambridge University Press
ISBN: 1316445054
Size: 63.36 MB
Format: PDF, ePub
View: 1863
Download and Read
This lively book lays out a methodology of confidence distributions and puts them through their paces. Among other merits, they lead to optimal combinations of confidence from different sources of information, and they can make complex models amenable to objective and indeed prior-free analysis for less subjectively inclined statisticians. The generous mixture of theory, illustrations, applications and exercises is suitable for statisticians at all levels of experience, as well as for data-oriented scientists. Some confidence distributions are less dispersed than their competitors. This concept leads to a theory of risk functions and comparisons for distributions of confidence. Neyman–Pearson type theorems leading to optimal confidence are developed and richly illustrated. Exact and optimal confidence distribution is the gold standard for inferred epistemic distributions. Confidence distributions and likelihood functions are intertwined, allowing prior distributions to be made part of the likelihood. Meta-analysis in likelihood terms is developed and taken beyond traditional methods, suiting it in particular to combining information across diverse data sources.

Brownian Motion

Author: Peter Mörters
Publisher: Cambridge University Press
ISBN: 1139486578
Size: 76.97 MB
Format: PDF, ePub, Docs
View: 6900
Download and Read
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
Publisher: Cambridge University Press
ISBN: 1139484605
Size: 40.33 MB
Format: PDF, Kindle
View: 6074
Download and Read
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.

Probabilistic Methods In Combinatorial Analysis

Author: Vladimir Nikolaevich Sachkov
Publisher: Cambridge University Press
ISBN: 9780521455121
Size: 40.40 MB
Format: PDF, Kindle
View: 3363
Download and Read
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
Size: 72.32 MB
Format: PDF, Docs
View: 2000
Download and Read
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.

Functional Analysis For Probability And Stochastic Processes

Author: Adam Bobrowski
Publisher: Cambridge University Press
ISBN: 9781139443883
Size: 60.80 MB
Format: PDF, Mobi
View: 2997
Download and Read
This text is designed both for students of probability and stochastic processes, and for students of functional analysis. For the reader not familiar with functional analysis a detailed introduction to necessary notions and facts is provided. However, this is not a straight textbook in functional analysis; rather, it presents some chosen parts of functional analysis that can help understand ideas from probability and stochastic processes. The subjects range from basic Hilbert and Banach spaces, through weak topologies and Banach algebras, to the theory of semigroups of bounded linear operators. Numerous standard and non-standard examples and exercises make the book suitable as a course textbook or for self-study.

Cambridge Tracts In Mathematics

Author: Jean Bertoin
Publisher: Cambridge University Press
ISBN: 9780521646321
Size: 68.12 MB
Format: PDF, ePub
View: 6550
Download and Read
This 1996 book is a comprehensive account of the theory of Lévy processes; aimed at probability theorists.