Statistical Modelling By Exponential Families
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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 | : 325 |
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 | : Rolf Sundberg |
Publisher | : Cambridge University Press |
Total Pages | : 297 |
Release | : 2019-08-29 |
Genre | : Mathematics |
ISBN | : 1108759912 |
This book is a readable, digestible introduction to exponential families, encompassing statistical models based on the most useful distributions in statistical theory, including the normal, gamma, binomial, Poisson, and negative binomial. Strongly motivated by applications, it presents the essential theory and then demonstrates the theory's practical potential by connecting it with developments in areas like item response analysis, social network models, conditional independence and latent variable structures, and point process models. Extensions to incomplete data models and generalized linear models are also included. In addition, the author gives a concise account of the philosophy of Per Martin-Löf in order to connect statistical modelling with ideas in statistical physics, including Boltzmann's law. Written for graduate students and researchers with a background in basic statistical inference, the book includes a vast set of examples demonstrating models for applications and exercises embedded within the text as well as at the ends of chapters.
Author | : Jeff Gill |
Publisher | : SAGE Publications |
Total Pages | : 135 |
Release | : 2000-08-07 |
Genre | : Social Science |
ISBN | : 1506320244 |
The author explains the theoretical underpinnings of generalized linear models so that researchers can decide how to select the best way to adapt their data for this type of analysis. Examples are provided to illustrate the application of GLM to actual data and the author includes his Web address where additional resources can be found.
Author | : Seth Sullivant |
Publisher | : American Mathematical Soc. |
Total Pages | : 506 |
Release | : 2018-11-19 |
Genre | : Education |
ISBN | : 1470435179 |
Algebraic statistics uses tools from algebraic geometry, commutative algebra, combinatorics, and their computational sides to address problems in statistics and its applications. The starting point for this connection is the observation that many statistical models are semialgebraic sets. The algebra/statistics connection is now over twenty years old, and this book presents the first broad introductory treatment of the subject. Along with background material in probability, algebra, and statistics, this book covers a range of topics in algebraic statistics including algebraic exponential families, likelihood inference, Fisher's exact test, bounds on entries of contingency tables, design of experiments, identifiability of hidden variable models, phylogenetic models, and model selection. With numerous examples, references, and over 150 exercises, this book is suitable for both classroom use and independent study.
Author | : Bernard P. Veldkamp |
Publisher | : Springer |
Total Pages | : 394 |
Release | : 2019-07-05 |
Genre | : Education |
ISBN | : 3030184803 |
This open access book presents a large number of innovations in the world of operational testing. It brings together different but related areas and provides insight in their possibilities, their advantages and drawbacks. The book not only addresses improvements in the quality of educational measurement, innovations in (inter)national large scale assessments, but also several advances in psychometrics and improvements in computerized adaptive testing, and it also offers examples on the impact of new technology in assessment. Due to its nature, the book will appeal to a broad audience within the educational measurement community. It contributes to both theoretical knowledge and also pays attention to practical implementation of innovations in testing technology.