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Author: Ronald W. Butler
Publisher: Cambridge University Press
ISBN: 1139466518
Category : Mathematics
Languages : en
Pages : 548
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Book Description
Modern statistical methods use complex, sophisticated models that can lead to intractable computations. Saddlepoint approximations can be the answer. Written from the user's point of view, this book explains in clear language how such approximate probability computations are made, taking readers from the very beginnings to current applications. The core material is presented in chapters 1-6 at an elementary mathematical level. Chapters 7-9 then give a highly readable account of higher-order asymptotic inference. Later chapters address areas where saddlepoint methods have had substantial impact: multivariate testing, stochastic systems and applied probability, bootstrap implementation in the transform domain, and Bayesian computation and inference. No previous background in the area is required. Data examples from real applications demonstrate the practical value of the methods. Ideal for graduate students and researchers in statistics, biostatistics, electrical engineering, econometrics, and applied mathematics, this is both an entry-level text and a valuable reference.
Author: Ronald W. Butler
Publisher: Cambridge University Press
ISBN: 1139466518
Category : Mathematics
Languages : en
Pages : 548
Get Book Here
Book Description
Modern statistical methods use complex, sophisticated models that can lead to intractable computations. Saddlepoint approximations can be the answer. Written from the user's point of view, this book explains in clear language how such approximate probability computations are made, taking readers from the very beginnings to current applications. The core material is presented in chapters 1-6 at an elementary mathematical level. Chapters 7-9 then give a highly readable account of higher-order asymptotic inference. Later chapters address areas where saddlepoint methods have had substantial impact: multivariate testing, stochastic systems and applied probability, bootstrap implementation in the transform domain, and Bayesian computation and inference. No previous background in the area is required. Data examples from real applications demonstrate the practical value of the methods. Ideal for graduate students and researchers in statistics, biostatistics, electrical engineering, econometrics, and applied mathematics, this is both an entry-level text and a valuable reference.
Author: Yue Kuen Kwok
Publisher: Springer
ISBN: 3319741012
Category : Mathematics
Languages : en
Pages : 134
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Book Description
This book summarizes recent advances in applying saddlepoint approximation methods to financial engineering. It addresses pricing exotic financial derivatives and calculating risk contributions to Value-at-Risk and Expected Shortfall in credit portfolios under various default correlation models. These standard problems involve the computation of tail probabilities and tail expectations of the corresponding underlying state variables. The text offers in a single source most of the saddlepoint approximation results in financial engineering, with different sets of ready-to-use approximation formulas. Much of this material may otherwise only be found in original research publications. The exposition and style are made rigorous by providing formal proofs of most of the results. Starting with a presentation of the derivation of a variety of saddlepoint approximation formulas in different contexts, this book will help new researchers to learn the fine technicalities of the topic. It will also be valuable to quantitative analysts in financial institutions who strive for effective valuation of prices of exotic financial derivatives and risk positions of portfolios of risky instruments.
Author: Jens Ledet Jensen
Publisher: Oxford University Press
ISBN: 9780198522959
Category : Mathematics
Languages : en
Pages : 348
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Book Description
This book explains the ideas behind the saddlepoint approximations as well as giving a detailed mathematical description of the subject and many worked out examples.
Author: Pamela Ann Ohman
Publisher:
ISBN:
Category :
Languages : en
Pages : 218
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Book Description
Author: Jens Ledet Jensen
Publisher:
ISBN:
Category : Approximation theory
Languages : en
Pages : 106
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Book Description
Author: Susan Tappero
Publisher:
ISBN:
Category : Linear operators
Languages : en
Pages : 158
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Book Description
Author: James E. Gentle
Publisher: Springer Science & Business Media
ISBN: 3642215513
Category : Computers
Languages : en
Pages : 1180
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Book Description
The Handbook of Computational Statistics - Concepts and Methods (second edition) is a revision of the first edition published in 2004, and contains additional comments and updated information on the existing chapters, as well as three new chapters addressing recent work in the field of computational statistics. This new edition is divided into 4 parts in the same way as the first edition. It begins with "How Computational Statistics became the backbone of modern data science" (Ch.1): an overview of the field of Computational Statistics, how it emerged as a separate discipline, and how its own development mirrored that of hardware and software, including a discussion of current active research. The second part (Chs. 2 - 15) presents several topics in the supporting field of statistical computing. Emphasis is placed on the need for fast and accurate numerical algorithms, and some of the basic methodologies for transformation, database handling, high-dimensional data and graphics treatment are discussed. The third part (Chs. 16 - 33) focuses on statistical methodology. Special attention is given to smoothing, iterative procedures, simulation and visualization of multivariate data. Lastly, a set of selected applications (Chs. 34 - 38) like Bioinformatics, Medical Imaging, Finance, Econometrics and Network Intrusion Detection highlight the usefulness of computational statistics in real-world applications.
Author: A. H. Welsh
Publisher: John Wiley & Sons
ISBN: 9780471115915
Category : Mathematics
Languages : en
Pages : 498
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Book Description
Relevant, concrete, and thorough--the essential data-based text onstatistical inference The ability to formulate abstract concepts and draw conclusionsfrom data is fundamental to mastering statistics. Aspects ofStatistical Inference equips advanced undergraduate and graduatestudents with a comprehensive grounding in statistical inference,including nonstandard topics such as robustness, randomization, andfinite population inference. A. H. Welsh goes beyond the standard texts and expertly synthesizesbroad, critical theory with concrete data and relevant topics. Thetext follows a historical framework, uses real-data sets andstatistical graphics, and treats multiparameter problems, yet isultimately about the concepts themselves. Written with clarity and depth, Aspects of Statistical Inference: * Provides a theoretical and historical grounding in statisticalinference that considers Bayesian, fiducial, likelihood, andfrequentist approaches * Illustrates methods with real-data sets on diabetic retinopathy,the pharmacological effects of caffeine, stellar velocity, andindustrial experiments * Considers multiparameter problems * Develops large sample approximations and shows how to use them * Presents the philosophy and application of robustness theory * Highlights the central role of randomization in statistics * Uses simple proofs to illuminate foundational concepts * Contains an appendix of useful facts concerning expansions,matrices, integrals, and distribution theory Here is the ultimate data-based text for comparing and presentingthe latest approaches to statistical inference.
Author: Joseph J.K. O Ruanaidh
Publisher: Springer Science & Business Media
ISBN: 1461207177
Category : Computers
Languages : en
Pages : 256
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Book Description
This book is concerned with the processing of signals that have been sam pled and digitized. The fundamental theory behind Digital Signal Process ing has been in existence for decades and has extensive applications to the fields of speech and data communications, biomedical engineering, acous tics, sonar, radar, seismology, oil exploration, instrumentation and audio signal processing to name but a few [87]. The term "Digital Signal Processing", in its broadest sense, could apply to any operation carried out on a finite set of measurements for whatever purpose. A book on signal processing would usually contain detailed de scriptions of the standard mathematical machinery often used to describe signals. It would also motivate an approach to real world problems based on concepts and results developed in linear systems theory, that make use of some rather interesting properties of the time and frequency domain representations of signals. While this book assumes some familiarity with traditional methods the emphasis is altogether quite different. The aim is to describe general methods for carrying out optimal signal processing.
Author: Philippe Flajolet
Publisher: Cambridge University Press
ISBN: 1139477161
Category : Mathematics
Languages : en
Pages : 825
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Book Description
Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. The theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines, including probability theory, statistical physics, computational biology, and information theory. With a careful combination of symbolic enumeration methods and complex analysis, drawing heavily on generating functions, results of sweeping generality emerge that can be applied in particular to fundamental structures such as permutations, sequences, strings, walks, paths, trees, graphs and maps. This account is the definitive treatment of the topic. The authors give full coverage of the underlying mathematics and a thorough treatment of both classical and modern applications of the theory. The text is complemented with exercises, examples, appendices and notes to aid understanding. The book can be used for an advanced undergraduate or a graduate course, or for self-study.
