Saddlepoint Approximations with Applications (Cambridge Series in Statistical and Probabilistic Mathematics, Series Number 22) 1st Edition by Ronald W. Butler (PDF)

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.

User’s Reviews

Editorial Reviews: Review “This compendious volume reflects an extraordinary amount of work and great attention to detail… The prose is clear, conversational, and occasionally enlivened with wry humor. The overall impression is of great readability. The author has set out to make saddlepoint approximations more accessible to the reader, aiming to simplify and clarify the sometimes turgid literature, and has succeeded admirably.” Andrew Robinson, University of Melbourne, Australia, Journal of Applied Statistics”This big book with its big coverage of a big topic is a big addition to the big Cambridge series.” Jordan Stoyanov, Newcastle University for the Journal of the Royal Statistical Society”This book is a welcome addition to the statistical literature. Saddlepoint Approximations With Applications provides an exhaustive and clear exposition of saddlepoint methods and their origins, derivations, and applications. I am disappointed that I did not have this book available when I first learned about saddlepoint approximations. It would have put me at a distinct advantage, shortening the time that it took me to learn about these methods and how to derive them. I expect it will serve as a valuable reference book in the years to come.” Pamela A. Ohman Strickland, Journal of the American Statistical Association Book Description This book explains how approximate probability calculations make complex models tractable, with clear, simple explanations and real data examples. About the Author Ronald W. Butler is Professor of Statistics at Colorado State University. His statistical work on prediction, likelihood methods, and saddlepoint methods is widely known. His more recent work concerns the study of complex stochastic systems, reliability, and survival analysis, with applications to electrical engineering and medical statistics. In applied mathematics, he has made important contributions to the approximation of hypergeometric functions with matrix and vector arguments. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐If ever have to apply probability (even at an elementary level) to engineering problems, sooner or later you will face the problem of approximating the “tail” of a probability distribution. Chernoff’s bound is an old favourite with communications engineers, and for good reason; but it is only a bound. The method of “Saddle point Approximation”, the central theme of this excellent text, gives you an asymptotic approximation to the correct value and not just a bound. The approximation is “asymptotic” in the same sense that Stirling’s formula is an “asymptotic” approximation to the factorial. In my opinion, Butler has written this book with the pedagogy of the educator and the sincerity of the practitioner. The book is copiously supplied with examples and exercises. Of course the book covers more than just “tail probabilities” as the “Saddle Point” technique has many applications in statistics including approximate likelihoods etc.

⭐The Book is awesome, I love it.

⭐

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