Author: Jürgen Pilz
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 316
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Book Description
Presents a clear treatment of the design and analysis of linear regression experiments in the presence of prior knowledge about the model parameters. Develops a unified approach to estimation and design; provides a Bayesian alternative to the least squares estimator; and indicates methods for the construction of optimal designs for the Bayes estimator. Material is also applicable to some well-known estimators using prior knowledge that is not available in the form of a prior distribution for the model parameters; such as mixed linear, minimax linear and ridge-type estimators.
Author: Salvatore J. Monaco
Publisher:
ISBN:
Category : Programming (Mathematics)
Languages : en
Pages : 111
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Book Description
A Bayesian approach to the design and analysis of experiments for linear regression models is presented, where the objectives of the experiment are satisfied by a joint design criterion reflecting concern for both model discrimination and parameter estimation. Under the assumption of unknown variance, a probability mixture representing the state of the system is formulated and the procedure sequentially selects design points which maximize the posterior marginal variance of the response surface. Several stopping rules for termination of the experiment are proposed and a number of simulations illustrating the use of this procedure are included. Some advantages of this procedure are that it is easily implemented as an on-line controller and allows the experimenter maximum flexibility in allocating resources and deciding when to terminate experimentation. (Author).
Author: Juergen PILZ
Publisher:
ISBN:
Category :
Languages : en
Pages : 216
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Book Description
Author: Ronald Christensen
Publisher: Springer Science & Business Media
ISBN: 9780387953618
Category : Mathematics
Languages : en
Pages : 502
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Book Description
This textbook provides a wide-ranging introduction to the use and theory of linear models for analyzing data. The author's emphasis is on providing a unified treatment of linear models, including analysis of variance models and regression models, based on projections, orthogonality, and other vector space ideas. Every chapter comes with numerous exercises and examples that make it ideal for a graduate-level course. All of the standard topics are covered in depth: ANOVA, estimation including Bayesian estimation, hypothesis testing, multiple comparisons, regression analysis, and experimental design models. In addition, the book covers topics that are not usually treated at this level, but which are important in their own right: balanced incomplete block designs, testing for lack of fit, testing for independence, models with singular covariance matrices, variance component estimation, best linear and best linear unbiased prediction, collinearity, and variable selection. This new edition includes discussion of identifiability and its relationship to estimability, different approaches to the theories of testing parametric hypotheses and analysis of covariance, additional discussion of the geometry of least squares estimation and testing, new discussion of models for experiments with factorial treatment structures, and a new appendix on possible causes for getting test statistics that are so small as to be suspicious. Ronald Christensen is a Professor of Statistics at the University of New Mexico. He is a Fellow of the American Statistical Association and the Institute of Mathematical Statistics.
Author: Ine Steyls
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: Martin Schmettow
Publisher: Springer
ISBN: 9783030463823
Category : Computers
Languages : en
Pages : 0
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Book Description
Design Research uses scientific methods to evaluate designs and build design theories. This book starts with recognizable questions in Design Research, such as A/B testing, how users learn to operate a device and why computer-generated faces are eerie. Using a broad range of examples, efficient research designs are presented together with statistical models and many visualizations. With the tidy R approach, producing publication-ready statistical reports is straight-forward and even non-programmers can learn this in just one day. Hundreds of illustrations, tables, simulations and models are presented with full R code and data included. Using Bayesian linear models, multi-level models and generalized linear models, an extensive statistical framework is introduced, covering a huge variety of research situations and yet, building on only a handful of basic concepts. Unique solutions to recurring problems are presented, such as psychometric multi-level models, beta regression for rating scales and ExGaussian regression for response times. A “think-first” approach is promoted for model building, as much as the quantitative interpretation of results, stimulating readers to think about data generating processes, as well as rational decision making. New Statistics for Design Researchers: A Bayesian Workflow in Tidy R targets scientists, industrial researchers and students in a range of disciplines, such as Human Factors, Applied Psychology, Communication Science, Industrial Design, Computer Science and Social Robotics. Statistical concepts are introduced in a problem-oriented way and with minimal formalism. Included primers on R and Bayesian statistics provide entry point for all backgrounds. A dedicated chapter on model criticism and comparison is a valuable addition for the seasoned scientist.
Author: Sung Chul Kim
Publisher:
ISBN:
Category :
Languages : en
Pages : 172
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Book Description
Author: Shucen Liu
Publisher:
ISBN:
Category : Automatic tracking
Languages : en
Pages : 90
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Book Description
In recent years, with widely accesses to powerful computers and development of new computing methods, Bayesian method has been applied to many fields including stock forecasting, machine learning, and genome data analysis. In this thesis, we will give an introduction to estimation methods for linear regression models including least square method, maximum likelihood method, and Bayesian method. We then describe Bayesian estimation for linear regression model in detail, and the prior and posterior distributions for different parameters will be derived. This method provides a posterior distribution of the parameters in the linear regression model, so that the uncertainties are integrated. Extensive experiments are conducted on simulated data and real-world data, and the results are compared to those of least square regression. Then we reached a conclusion that Bayesian approach has a better performance when the sample size is large.
Author: Broemeling
Publisher: CRC Press
ISBN: 1351464485
Category : Mathematics
Languages : en
Pages : 472
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Book Description
With Bayesian statistics rapidly becoming accepted as a way to solve applied statisticalproblems, the need for a comprehensive, up-to-date source on the latest advances in thisfield has arisen.Presenting the basic theory of a large variety of linear models from a Bayesian viewpoint,Bayesian Analysis of Linear Models fills this need. Plus, this definitive volume containssomething traditional-a review of Bayesian techniques and methods of estimation, hypothesis,testing, and forecasting as applied to the standard populations ... somethinginnovative-a new approach to mixed models and models not generally studied by statisticianssuch as linear dynamic systems and changing parameter models ... and somethingpractical-clear graphs, eary-to-understand examples, end-of-chapter problems, numerousreferences, and a distribution appendix.Comprehensible, unique, and in-depth, Bayesian Analysis of Linear Models is the definitivemonograph for statisticians, econometricians, and engineers. In addition, this text isideal for students in graduate-level courses such as linear models, econometrics, andBayesian inference.
Author: Scott M. Lynch
Publisher: Springer Science & Business Media
ISBN: 0387712658
Category : Social Science
Languages : en
Pages : 376
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Book Description
This book outlines Bayesian statistical analysis in great detail, from the development of a model through the process of making statistical inference. The key feature of this book is that it covers models that are most commonly used in social science research - including the linear regression model, generalized linear models, hierarchical models, and multivariate regression models - and it thoroughly develops each real-data example in painstaking detail.
