Download or read book Statistical Modelling by Exponential Families written by Rolf Sundberg and published by Cambridge University Press. This book was released on 2019-08-29 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: A readable, digestible introduction to essential theory and wealth of applications, with a vast set of examples and numerous exercises.
Download or read book Graphical Models Exponential Families and Variational Inference written by Martin J. Wainwright and published by Now Publishers Inc. This book was released on 2008 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Exponential Family Nonlinear Models written by Bo-Cheng Wei and published by . This book was released on 1998-09 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Statistical Modelling by Exponential Families written by Rolf Sundberg and published by Cambridge University Press. This book was released on 2019-08-29 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Fundamentals of Statistical Exponential Families written by Lawrence D. Brown and published by IMS. This book was released on 1986 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Generalized Linear Models written by Jeff Gill and published by SAGE Publications. This book was released on 2000-08-07 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Algebraic Statistics written by Seth Sullivant and published by American Mathematical Soc.. This book was released on 2018-11-19 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Statistical Modelling in GLIM written by Murray A. Aitkin and published by Oxford University Press. This book was released on 1989 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Theory of Dispersion Models written by Bent Jorgensen and published by CRC Press. This book was released on 1997-06-01 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of dispersion models straddles both statistics and probability, and involves an encyclopedic collection of tools, such as exponential families, asymptotic theory, stochastic processes, Tauber theory, infinite divisibility, and stable distributions. The Theory of Dispersion Models introduces the reader to these models, which serve as error distributions for generalized linear models, and looks at their applications within this context.
Download or read book Introduction to Statistical Modelling written by Annette J. Dobson and published by Springer. This book was released on 2013-11-11 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Dynamical Biostatistical Models written by Daniel Commenges and published by CRC Press. This book was released on 2015-10-02 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dynamical Biostatistical Models presents statistical models and methods for the analysis of longitudinal data. The book focuses on models for analyzing repeated measures of quantitative and qualitative variables and events history, including survival and multistate models. Most of the advanced methods, such as multistate and joint models, can be ap
Download or read book Sufficient Dimension Reduction written by Bing Li and published by CRC Press. This book was released on 2018-04-27 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sufficient dimension reduction is a rapidly developing research field that has wide applications in regression diagnostics, data visualization, machine learning, genomics, image processing, pattern recognition, and medicine, because they are fields that produce large datasets with a large number of variables. Sufficient Dimension Reduction: Methods and Applications with R introduces the basic theories and the main methodologies, provides practical and easy-to-use algorithms and computer codes to implement these methodologies, and surveys the recent advances at the frontiers of this field. Features Provides comprehensive coverage of this emerging research field. Synthesizes a wide variety of dimension reduction methods under a few unifying principles such as projection in Hilbert spaces, kernel mapping, and von Mises expansion. Reflects most recent advances such as nonlinear sufficient dimension reduction, dimension folding for tensorial data, as well as sufficient dimension reduction for functional data. Includes a set of computer codes written in R that are easily implemented by the readers. Uses real data sets available online to illustrate the usage and power of the described methods. Sufficient dimension reduction has undergone momentous development in recent years, partly due to the increased demands for techniques to process high-dimensional data, a hallmark of our age of Big Data. This book will serve as the perfect entry into the field for the beginning researchers or a handy reference for the advanced ones. The author Bing Li obtained his Ph.D. from the University of Chicago. He is currently a Professor of Statistics at the Pennsylvania State University. His research interests cover sufficient dimension reduction, statistical graphical models, functional data analysis, machine learning, estimating equations and quasilikelihood, and robust statistics. He is a fellow of the Institute of Mathematical Statistics and the American Statistical Association. He is an Associate Editor for The Annals of Statistics and the Journal of the American Statistical Association.
Download or read book Conditional Specification of Statistical Models written by Barry C. Arnold and published by Springer Science & Business Media. This book was released on 2007-06-02 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: Efforts to visualize multivariate densities necessarily involve the use of cross-sections, or, equivalently, conditional densities. This book focuses on distributions that are completely specified in terms of conditional densities. They are appropriately used in any modeling situation where conditional information is completely or partially available. All statistical researchers seeking more flexible models than those provided by classical models will find conditionally specified distributions of interest.
Download or read book Probability and Statistical Models written by Arjun K. Gupta and published by Springer Science & Business Media. This book was released on 2010-08-26 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Mathematical Statistics written by Richard J. Rossi and published by John Wiley & Sons. This book was released on 2018-06-14 with total page 611 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents a unified approach to parametric estimation, confidence intervals, hypothesis testing, and statistical modeling, which are uniquely based on the likelihood function This book addresses mathematical statistics for upper-undergraduates and first year graduate students, tying chapters on estimation, confidence intervals, hypothesis testing, and statistical models together to present a unifying focus on the likelihood function. It also emphasizes the important ideas in statistical modeling, such as sufficiency, exponential family distributions, and large sample properties. Mathematical Statistics: An Introduction to Likelihood Based Inference makes advanced topics accessible and understandable and covers many topics in more depth than typical mathematical statistics textbooks. It includes numerous examples, case studies, a large number of exercises ranging from drill and skill to extremely difficult problems, and many of the important theorems of mathematical statistics along with their proofs. In addition to the connected chapters mentioned above, Mathematical Statistics covers likelihood-based estimation, with emphasis on multidimensional parameter spaces and range dependent support. It also includes a chapter on confidence intervals, which contains examples of exact confidence intervals along with the standard large sample confidence intervals based on the MLE's and bootstrap confidence intervals. There’s also a chapter on parametric statistical models featuring sections on non-iid observations, linear regression, logistic regression, Poisson regression, and linear models. Prepares students with the tools needed to be successful in their future work in statistics data science Includes practical case studies including real-life data collected from Yellowstone National Park, the Donner party, and the Titanic voyage Emphasizes the important ideas to statistical modeling, such as sufficiency, exponential family distributions, and large sample properties Includes sections on Bayesian estimation and credible intervals Features examples, problems, and solutions Mathematical Statistics: An Introduction to Likelihood Based Inference is an ideal textbook for upper-undergraduate and graduate courses in probability, mathematical statistics, and/or statistical inference.
Download or read book Statistical Modeling and Computation written by Dirk P. Kroese and published by Springer Science & Business Media. This book was released on 2013-11-18 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook on statistical modeling and statistical inference will assist advanced undergraduate and graduate students. Statistical Modeling and Computation provides a unique introduction to modern Statistics from both classical and Bayesian perspectives. It also offers an integrated treatment of Mathematical Statistics and modern statistical computation, emphasizing statistical modeling, computational techniques, and applications. Each of the three parts will cover topics essential to university courses. Part I covers the fundamentals of probability theory. In Part II, the authors introduce a wide variety of classical models that include, among others, linear regression and ANOVA models. In Part III, the authors address the statistical analysis and computation of various advanced models, such as generalized linear, state-space and Gaussian models. Particular attention is paid to fast Monte Carlo techniques for Bayesian inference on these models. Throughout the book the authors include a large number of illustrative examples and solved problems. The book also features a section with solutions, an appendix that serves as a MATLAB primer, and a mathematical supplement.
Download or read book A Survey of Statistical Network Models written by Anna Goldenberg and published by Now Publishers Inc. This book was released on 2010 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: Networks are ubiquitous in science and have become a focal point for discussion in everyday life. Formal statistical models for the analysis of network data have emerged as a major topic of interest in diverse areas of study, and most of these involve a form of graphical representation. Probability models on graphs date back to 1959. Along with empirical studies in social psychology and sociology from the 1960s, these early works generated an active network community and a substantial literature in the 1970s. This effort moved into the statistical literature in the late 1970s and 1980s, and the past decade has seen a burgeoning network literature in statistical physics and computer science. The growth of the World Wide Web and the emergence of online networking communities such as Facebook, MySpace, and LinkedIn, and a host of more specialized professional network communities has intensified interest in the study of networks and network data. Our goal in this review is to provide the reader with an entry point to this burgeoning literature. We begin with an overview of the historical development of statistical network modeling and then we introduce a number of examples that have been studied in the network literature. Our subsequent discussion focuses on a number of prominent static and dynamic network models and their interconnections. We emphasize formal model descriptions, and pay special attention to the interpretation of parameters and their estimation. We end with a description of some open problems and challenges for machine learning and statistics.
