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| Author | : Rolf Sundberg |
| Publisher | : Cambridge University Press |
| Total Pages | : 297 |
| Release | : 2019-08-29 |
| Genre | : Business & Economics |
| ISBN | : 1108476597 |
A readable, digestible introduction to essential theory and wealth of applications, with a vast set of examples and numerous exercises.
| Author | : Stefan Bedbur |
| Publisher | : Springer Nature |
| Total Pages | : 147 |
| Release | : 2021-10-07 |
| Genre | : Mathematics |
| ISBN | : 3030819000 |
This book provides a concise introduction to exponential families. Parametric families of probability distributions and their properties are extensively studied in the literature on statistical modeling and inference. Exponential families of distributions comprise density functions of a particular form, which enables general assertions and leads to nice features. With a focus on parameter estimation and hypotheses testing, the text introduces the reader to distributional and statistical properties of multivariate and multiparameter exponential families along with a variety of detailed examples. The material is widely self-contained and written in a mathematical setting. It may serve both as a concise, mathematically rigorous course on exponential families in a systematic structure and as an introduction to Mathematical Statistics restricted to the use of exponential families.
| Author | : Uwe Küchler |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 322 |
| Release | : 2006-05-09 |
| Genre | : Mathematics |
| ISBN | : 0387227652 |
A comprehensive account of the statistical theory of exponential families of stochastic processes. The book reviews the progress in the field made over the last ten years or so by the authors - two of the leading experts in the field - and several other researchers. The theory is applied to a broad spectrum of examples, covering a large number of frequently applied stochastic process models with discrete as well as continuous time. To make the reading even easier for statisticians with only a basic background in the theory of stochastic process, the first part of the book is based on classical theory of stochastic processes only, while stochastic calculus is used later. Most of the concepts and tools from stochastic calculus needed when working with inference for stochastic processes are introduced and explained without proof in an appendix. This appendix can also be used independently as an introduction to stochastic calculus for statisticians. Numerous exercises are also included.
| Author | : Martin J. Wainwright |
| Publisher | : Now Publishers Inc |
| Total Pages | : 324 |
| Release | : 2008 |
| Genre | : Computers |
| ISBN | : 1601981848 |
The core of this paper is a general set of variational principles for the problems of computing marginal probabilities and modes, applicable to multivariate statistical models in the exponential family.
| Author | : Lawrence D. Brown |
| Publisher | : IMS |
| Total Pages | : 302 |
| Release | : 1986 |
| Genre | : Business & Economics |
| ISBN | : 9780940600102 |
| Author | : Bo-Cheng Wei |
| Publisher | : |
| Total Pages | : 248 |
| Release | : 1998-09 |
| Genre | : Mathematics |
| ISBN | : |
This book gives a comprehensive introduction to exponential family nonlinear models, which are the natural extension of generalized linear models and normal nonlinear regression models. The differential geometric framework is presented for these models and geometric methods are widely used in this book. This book is ideally suited for researchers in statistical interfaces and graduate students with a basic knowledge of statistics.
| Author | : Annette J. Dobson |
| Publisher | : Springer |
| Total Pages | : 133 |
| Release | : 2013-11-11 |
| Genre | : Mathematics |
| ISBN | : 1489931740 |
This book is about generalized linear models as described by NeIder and Wedderburn (1972). This approach provides a unified theoretical and computational framework for the most commonly used statistical methods: regression, analysis of variance and covariance, logistic regression, log-linear models for contingency tables and several more specialized techniques. More advanced expositions of the subject are given by McCullagh and NeIder (1983) and Andersen (1980). The emphasis is on the use of statistical models to investigate substantive questions rather than to produce mathematical descriptions of the data. Therefore parameter estimation and hypothesis testing are stressed. I have assumed that the reader is familiar with the most commonly used statistical concepts and methods and has some basic knowledge of calculus and matrix algebra. Short numerical examples are used to illustrate the main points. In writing this book I have been helped greatly by the comments and criticism of my students and colleagues, especially Anne Young. However, the choice of material, and the obscurities and errors are my responsibility and I apologize to the reader for any irritation caused by them. For typing the manuscript under difficult conditions I am grateful to Anne McKim, Jan Garnsey, Cath Claydon and Julie Latimer.
| Author | : Arjun K. Gupta |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 267 |
| Release | : 2010-08-26 |
| Genre | : Mathematics |
| ISBN | : 0817649875 |
With an emphasis on models and techniques, this textbook introduces many of the fundamental concepts of stochastic modeling that are now a vital component of almost every scientific investigation. In particular, emphasis is placed on laying the foundation for solving problems in reliability, insurance, finance, and credit risk. The material has been carefully selected to cover the basic concepts and techniques on each topic, making this an ideal introductory gateway to more advanced learning. With exercises and solutions to selected problems accompanying each chapter, this textbook is for a wide audience including advanced undergraduate and beginning-level graduate students, researchers, and practitioners in mathematics, statistics, engineering, and economics.
| Author | : Ronald W. Butler |
| Publisher | : Cambridge University Press |
| Total Pages | : 548 |
| Release | : 2007-08-16 |
| Genre | : Mathematics |
| ISBN | : 1139466518 |
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 | : Murray A. Aitkin |
| Publisher | : Oxford University Press |
| Total Pages | : 390 |
| Release | : 1989 |
| Genre | : Mathematics |
| ISBN | : 9780198522034 |
The analysis of data by statistical modelling is becoming increasingly important. This book presents both the theory of statistical modelling with generalized linear models and the application of the theory to practical problems using the widely available package GLIM. The authors have takenpains to integrate the theory with many practical examples which illustrate the value of interactive statistical modelling. Throughout the book theoretical issues of formulating and simplifying models are discussed, as are problems of validating the models by the detection of outliers and influential observations. The book arises from short courses given at the University of Lancaster's Centre for Applied Statistics, with an emphasis on practical programming in GLIM and numerous examples. A wide range of case studies is provided, using the normal, binomial, Poisson, multinomial, gamma, exponential andWeibull distributions. A feature of the book is a detailed discussion of survival analysis. Statisticians working in a wide range of fields, including biomedical and social sciences, will find this book an invaluable desktop companion to aid their statistical modelling. It will also provide a text for students meeting the ideas of statistical modelling for the first time.
