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Author : Gerda Claeskens,Nils Lid Hjort
Publisher : Unknown
Page : 312 pages
File Size : 53,6 Mb
Release : 2008-07-28
Category : Mathematics
ISBN : 0521852250
First book to synthesize the research and practice from the active field of model selection.
Author : Gerda Claeskens,Nils Lid Hjort
Publisher : Cambridge University Press
Page : 312 pages
File Size : 41,5 Mb
Release : 2008-07-28
Category : Mathematics
ISBN : 9781139471800
Given a data set, you can fit thousands of models at the push of a button, but how do you choose the best? With so many candidate models, overfitting is a real danger. Is the monkey who typed Hamlet actually a good writer? Choosing a model is central to all statistical work with data. We have seen rapid advances in model fitting and in the theoretical understanding of model selection, yet this book is the first to synthesize research and practice from this active field. Model choice criteria are explained, discussed and compared, including the AIC, BIC, DIC and FIC. The uncertainties involved with model selection are tackled, with discussions of frequentist and Bayesian methods; model averaging schemes are presented. Real-data examples are complemented by derivations providing deeper insight into the methodology, and instructive exercises build familiarity with the methods. The companion website features Data sets and R code.
Author : Kenneth P. Burnham,David R. Anderson
Publisher : Springer Science & Business Media
Page : 373 pages
File Size : 53,8 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781475729177
Statisticians and applied scientists must often select a model to fit empirical data. This book discusses the philosophy and strategy of selecting such a model using the information theory approach pioneered by Hirotugu Akaike. This approach focuses critical attention on a priori modeling and the selection of a good approximating model that best represents the inference supported by the data. The book includes practical applications in biology and environmental science.
Author : Kenneth P. Burnham,David R. Anderson
Publisher : Springer Science & Business Media
Page : 488 pages
File Size : 52,7 Mb
Release : 2007-05-28
Category : Mathematics
ISBN : 9780387224565
A unique and comprehensive text on the philosophy of model-based data analysis and strategy for the analysis of empirical data. The book introduces information theoretic approaches and focuses critical attention on a priori modeling and the selection of a good approximating model that best represents the inference supported by the data. It contains several new approaches to estimating model selection uncertainty and incorporating selection uncertainty into estimates of precision. An array of examples is given to illustrate various technical issues. The text has been written for biologists and statisticians using models for making inferences from empirical data.
Author : Göran Kauermann,Helmut Küchenhoff,Christian Heumann
Publisher : Springer Nature
Page : 361 pages
File Size : 41,9 Mb
Release : 2021-09-30
Category : Mathematics
ISBN : 9783030698270
This textbook provides a comprehensive introduction to statistical principles, concepts and methods that are essential in modern statistics and data science. The topics covered include likelihood-based inference, Bayesian statistics, regression, statistical tests and the quantification of uncertainty. Moreover, the book addresses statistical ideas that are useful in modern data analytics, including bootstrapping, modeling of multivariate distributions, missing data analysis, causality as well as principles of experimental design. The textbook includes sufficient material for a two-semester course and is intended for master’s students in data science, statistics and computer science with a rudimentary grasp of probability theory. It will also be useful for data science practitioners who want to strengthen their statistics skills.
Author : Claeskens Gerda Hjort Nils Lid,Gerda Claeskens,Nils Lid Hjort
Publisher : Unknown
Page : 332 pages
File Size : 52,9 Mb
Release : 2014-05-14
Category : Mathematics
ISBN : 0511424108
Author : Tomohiro Ando
Publisher : CRC Press
Page : 300 pages
File Size : 43,9 Mb
Release : 2010-05-27
Category : Mathematics
ISBN : 1439836159
Along with many practical applications, Bayesian Model Selection and Statistical Modeling presents an array of Bayesian inference and model selection procedures. It thoroughly explains the concepts, illustrates the derivations of various Bayesian model selection criteria through examples, and provides R code for implementation. The author shows how to implement a variety of Bayesian inference using R and sampling methods, such as Markov chain Monte Carlo. He covers the different types of simulation-based Bayesian model selection criteria, including the numerical calculation of Bayes factors, the Bayesian predictive information criterion, and the deviance information criterion. He also provides a theoretical basis for the analysis of these criteria. In addition, the author discusses how Bayesian model averaging can simultaneously treat both model and parameter uncertainties. Selecting and constructing the appropriate statistical model significantly affect the quality of results in decision making, forecasting, stochastic structure explorations, and other problems. Helping you choose the right Bayesian model, this book focuses on the framework for Bayesian model selection and includes practical examples of model selection criteria.
Author : Han Hong,Bruce Preston
Publisher : Unknown
Page : 29 pages
File Size : 48,8 Mb
Release : 2008
Category : Bayesian statistical decision theory
ISBN : OCLC:244821047
This paper studies the asymptotic relationship between Bayesian model averaging and post-selection frequentist predictors in both nested and nonnested models. We derive conditions under which their difference is of a smaller order of magnitude than the inverse of the square root of the sample size in large samples. This result depends crucially on the relation between posterior odds and frequentist model selection criteria. Weak conditions are given under which consistent model selection is feasible, regardless of whether models are nested or nonnested and regardless of whether models are correctly specified or not, in the sense that they select the best model with the least number of parameters with probability converging to 1. Under these conditions, Bayesian posterior odds and BICs are consistent for selecting among nested models, but are not consistent for selecting among nonnested models.
Author : David Fletcher
Publisher : Springer
Page : 107 pages
File Size : 55,6 Mb
Release : 2019-01-17
Category : Mathematics
ISBN : 9783662585412
This book provides a concise and accessible overview of model averaging, with a focus on applications. Model averaging is a common means of allowing for model uncertainty when analysing data, and has been used in a wide range of application areas, such as ecology, econometrics, meteorology and pharmacology. The book presents an overview of the methods developed in this area, illustrating many of them with examples from the life sciences involving real-world data. It also includes an extensive list of references and suggestions for further research. Further, it clearly demonstrates the links between the methods developed in statistics, econometrics and machine learning, as well as the connection between the Bayesian and frequentist approaches to model averaging. The book appeals to statisticians and scientists interested in what methods are available, how they differ and what is known about their properties. It is assumed that readers are familiar with the basic concepts of statistical theory and modelling, including probability, likelihood and generalized linear models.
Author : Anonim
Publisher : Cuvillier Verlag
Page : 182 pages
File Size : 43,6 Mb
Release : 2006-04-24
Category : Science
ISBN : 9783736918443
Most applied statistical analyses are carried out under model uncertainty, meaning that the model which generated the observations is unknown, and so the data are first used to select one of a set of plausible models by means of some selection criterion. Generally the data are then used to make inferences about some quantity of interest, ignoring model selection uncertainty, i.e. the fact that the selection step was carried out using the same data, and despite the known fact that this leads to invalid inferences. This thesis investigates several issues relating to this problem from both the Bayesian and the frequentist points of view, and offers new suggestions for dealing with it. We examine Bayesian model averaging (BMA) and point out that its frequentist performance is not always well-defined because, in some cases, it is unclear whether BMA methodology is truly Bayesian. We illustrate the point with a “fully Bayesian model averaging" that is applicable when the quantity of interest is parametric.
Author : Allan D. R. McQuarrie,Chih-Ling Tsai
Publisher : World Scientific
Page : 479 pages
File Size : 41,9 Mb
Release : 1998
Category : Mathematics
ISBN : 9789812385451
This important book describes procedures for selecting a model from a large set of competing statistical models. It includes model selection techniques for univariate and multivariate regression models, univariate and multivariate autoregressive models, nonparametric (including wavelets) and semiparametric regression models, and quasi-likelihood and robust regression models. Information-based model selection criteria are discussed, and small sample and asymptotic properties are presented. The book also provides examples and large scale simulation studies comparing the performances of information-based model selection criteria, bootstrapping, and cross-validation selection methods over a wide range of models.
Author : National Research Council,Division on Earth and Life Studies,Board on Environmental Studies and Toxicology,Committee on Models in the Regulatory Decision Process
Publisher : National Academies Press
Page : 286 pages
File Size : 42,7 Mb
Release : 2007-08-25
Category : Political Science
ISBN : 9780309110006
Many regulations issued by the U.S. Environmental Protection Agency (EPA) are based on the results of computer models. Models help EPA explain environmental phenomena in settings where direct observations are limited or unavailable, and anticipate the effects of agency policies on the environment, human health and the economy. Given the critical role played by models, the EPA asked the National Research Council to assess scientific issues related to the agency's selection and use of models in its decisions. The book recommends a series of guidelines and principles for improving agency models and decision-making processes. The centerpiece of the book's recommended vision is a life-cycle approach to model evaluation which includes peer review, corroboration of results, and other activities. This will enhance the agency's ability to respond to requirements from a 2001 law on information quality and improve policy development and implementation.
Author : Sadanori Konishi,Genshiro Kitagawa
Publisher : Springer Science & Business Media
Page : 282 pages
File Size : 50,9 Mb
Release : 2008
Category : Business & Economics
ISBN : 9780387718866
Statistical modeling is a critical tool in scientific research. This book provides comprehensive explanations of the concepts and philosophy of statistical modeling, together with a wide range of practical and numerical examples. The authors expect this work to be of great value not just to statisticians but also to researchers and practitioners in various fields of research such as information science, computer science, engineering, bioinformatics, economics, marketing and environmental science. It’s a crucial area of study, as statistical models are used to understand phenomena with uncertainty and to determine the structure of complex systems. They’re also used to control such systems, as well as to make reliable predictions in various natural and social science fields.
Author : Andrew Gelman,John B. Carlin,Hal S. Stern,David B. Dunson,Aki Vehtari,Donald B. Rubin
Publisher : CRC Press
Page : 677 pages
File Size : 45,6 Mb
Release : 2013-11-01
Category : Mathematics
ISBN : 9781439840955
Now in its third edition, this classic book is widely considered the leading text on Bayesian methods, lauded for its accessible, practical approach to analyzing data and solving research problems. Bayesian Data Analysis, Third Edition continues to take an applied approach to analysis using up-to-date Bayesian methods. The authors—all leaders in the statistics community—introduce basic concepts from a data-analytic perspective before presenting advanced methods. Throughout the text, numerous worked examples drawn from real applications and research emphasize the use of Bayesian inference in practice. New to the Third Edition Four new chapters on nonparametric modeling Coverage of weakly informative priors and boundary-avoiding priors Updated discussion of cross-validation and predictive information criteria Improved convergence monitoring and effective sample size calculations for iterative simulation Presentations of Hamiltonian Monte Carlo, variational Bayes, and expectation propagation New and revised software code The book can be used in three different ways. For undergraduate students, it introduces Bayesian inference starting from first principles. For graduate students, the text presents effective current approaches to Bayesian modeling and computation in statistics and related fields. For researchers, it provides an assortment of Bayesian methods in applied statistics. Additional materials, including data sets used in the examples, solutions to selected exercises, and software instructions, are available on the book’s web page.
Author : Allan D. R. McQuarrie,Chih-Ling Tsai
Publisher : World Scientific
Page : 479 pages
File Size : 52,7 Mb
Release : 1998
Category : Mathematics
ISBN : 9789810232429
This important book describes procedures for selecting a model from a large set of competing statistical models. It includes model selection techniques for univariate and multivariate regression models, univariate and multivariate autoregressive models, nonparametric (including wavelets) and semiparametric regression models, and quasi-likelihood and robust regression models. Information-based model selection criteria are discussed, and small sample and asymptotic properties are presented. The book also provides examples and large scale simulation studies comparing the performances of information-based model selection criteria, bootstrapping, and cross-validation selection methods over a wide range of models.