Download or read book Bayesian Estimation and Experimental Design in Linear Regression Models written by Jürgen Pilz and published by . This book was released on 1991-07-09 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book A Bayesian Approach to the Design and Analysis of Experiments for Regression Models written by Salvatore J. Monaco and published by . This book was released on 1974 with total page 111 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).

Download or read book Bayesian Estimation and Experimetal Design in Linear Regression Models written by Juergen PILZ and published by . This book was released on 1983 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Plane Answers to Complex Questions written by Ronald Christensen and published by Springer Nature. This book was released on 2020-03-13 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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: estimation including biased and Bayesian estimation, significance testing, ANOVA, 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: best linear and best linear unbiased prediction, split plot models, balanced incomplete block designs, testing for lack of fit, testing for independence, models with singular covariance matrices, diagnostics, collinearity, and variable selection. This new edition includes new sections on alternatives to least squares estimation and the variance-bias tradeoff, expanded discussion of variable selection, new material on characterizing the interaction space in an unbalanced two-way ANOVA, Freedman's critique of the sandwich estimator, and much more.

Download or read book Bayesian Optimal Experimental Design written by Ine Steyls and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book New Statistics for Design Researchers written by Martin Schmettow and published by Springer. This book was released on 2022-07-15 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Bayesian Calibration Experimental Designs Based on Linear Models written by Sung Chul Kim and published by . This book was released on 1988 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Bayesian Inference in Linear Regression Models written by Shucen Liu and published by . This book was released on 2012 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Optimal Experimental Design written by Jesús López-Fidalgo and published by Springer Nature. This book was released on 2023-10-14 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides a concise introduction to optimal experimental design and efficiently prepares the reader for research in the area. It presents the common concepts and techniques for linear and nonlinear models as well as Bayesian optimal designs. The last two chapters are devoted to particular themes of interest, including recent developments and hot topics in optimal experimental design, and real-world applications. Numerous examples and exercises are included, some of them with solutions or hints, as well as references to the existing software for computing designs. The book is primarily intended for graduate students and young researchers in statistics and applied mathematics who are new to the field of optimal experimental design. Given the applications and the way concepts and results are introduced, parts of the text will also appeal to engineers and other applied researchers.

Download or read book Bayesian Analysis of Linear Models written by Broemeling and published by CRC Press. This book was released on 2017-11-22 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Experimental Design and Data Analysis for Biologists written by Gerry P. Quinn and published by Cambridge University Press. This book was released on 2002-03-21 with total page 851 pages. Available in PDF, EPUB and Kindle. Book excerpt: An essential textbook for any student or researcher in biology needing to design experiments, sample programs or analyse the resulting data. The text begins with a revision of estimation and hypothesis testing methods, covering both classical and Bayesian philosophies, before advancing to the analysis of linear and generalized linear models. Topics covered include linear and logistic regression, simple and complex ANOVA models (for factorial, nested, block, split-plot and repeated measures and covariance designs), and log-linear models. Multivariate techniques, including classification and ordination, are then introduced. Special emphasis is placed on checking assumptions, exploratory data analysis and presentation of results. The main analyses are illustrated with many examples from published papers and there is an extensive reference list to both the statistical and biological literature. The book is supported by a website that provides all data sets, questions for each chapter and links to software.

Download or read book Introduction to Applied Bayesian Statistics and Estimation for Social Scientists written by Scott M. Lynch and published by Springer Science & Business Media. This book was released on 2007-06-30 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Applied Multivariate Data Analysis written by J.D. Jobson and published by Springer. This book was released on 1999-02-11 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: An easy to read survey of data analysis, linear regression models and analysis of variance. The extensive development of the linear model includes the use of the linear model approach to analysis of variance provides a strong link to statistical software packages, and is complemented by a thorough overview of theory. It is assumed that the reader has the background equivalent to an introductory book in statistical inference. Can be read easily by those who have had brief exposure to calculus and linear algebra. Intended for first year graduate students in business, social and the biological sciences. Provides the student with the necessary statistics background for a course in research methodology. In addition, undergraduate statistics majors will find this text useful as a survey of linear models and their applications.

Download or read book Linear Models in Statistics written by Alvin C. Rencher and published by John Wiley & Sons. This book was released on 2008-01-07 with total page 690 pages. Available in PDF, EPUB and Kindle. Book excerpt: The essential introduction to the theory and application of linear models—now in a valuable new edition Since most advanced statistical tools are generalizations of the linear model, it is neces-sary to first master the linear model in order to move forward to more advanced concepts. The linear model remains the main tool of the applied statistician and is central to the training of any statistician regardless of whether the focus is applied or theoretical. This completely revised and updated new edition successfully develops the basic theory of linear models for regression, analysis of variance, analysis of covariance, and linear mixed models. Recent advances in the methodology related to linear mixed models, generalized linear models, and the Bayesian linear model are also addressed. Linear Models in Statistics, Second Edition includes full coverage of advanced topics, such as mixed and generalized linear models, Bayesian linear models, two-way models with empty cells, geometry of least squares, vector-matrix calculus, simultaneous inference, and logistic and nonlinear regression. Algebraic, geometrical, frequentist, and Bayesian approaches to both the inference of linear models and the analysis of variance are also illustrated. Through the expansion of relevant material and the inclusion of the latest technological developments in the field, this book provides readers with the theoretical foundation to correctly interpret computer software output as well as effectively use, customize, and understand linear models. This modern Second Edition features: New chapters on Bayesian linear models as well as random and mixed linear models Expanded discussion of two-way models with empty cells Additional sections on the geometry of least squares Updated coverage of simultaneous inference The book is complemented with easy-to-read proofs, real data sets, and an extensive bibliography. A thorough review of the requisite matrix algebra has been addedfor transitional purposes, and numerous theoretical and applied problems have been incorporated with selected answers provided at the end of the book. A related Web site includes additional data sets and SAS® code for all numerical examples. Linear Model in Statistics, Second Edition is a must-have book for courses in statistics, biostatistics, and mathematics at the upper-undergraduate and graduate levels. It is also an invaluable reference for researchers who need to gain a better understanding of regression and analysis of variance.

Download or read book Handbook of Design and Analysis of Experiments written by Angela Dean and published by CRC Press. This book was released on 2015-06-26 with total page 946 pages. Available in PDF, EPUB and Kindle. Book excerpt: This carefully edited collection synthesizes the state of the art in the theory and applications of designed experiments and their analyses. It provides a detailed overview of the tools required for the optimal design of experiments and their analyses. The handbook covers many recent advances in the field, including designs for nonlinear models and algorithms applicable to a wide variety of design problems. It also explores the extensive use of experimental designs in marketing, the pharmaceutical industry, engineering and other areas.

Download or read book Sequential Analysis and Optimal Design written by Herman Chernoff and published by SIAM. This book was released on 1972-01-01 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: An exploration of the interrelated fields of design of experiments and sequential analysis with emphasis on the nature of theoretical statistics and how this relates to the philosophy and practice of statistics.

Download or read book Contemporary Experimental Design Multivariate Analysis and Data Mining written by Jianqing Fan and published by Springer Nature. This book was released on 2020-05-22 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: The collection and analysis of data play an important role in many fields of science and technology, such as computational biology, quantitative finance, information engineering, machine learning, neuroscience, medicine, and the social sciences. Especially in the era of big data, researchers can easily collect data characterised by massive dimensions and complexity. In celebration of Professor Kai-Tai Fang’s 80th birthday, we present this book, which furthers new and exciting developments in modern statistical theories, methods and applications. The book features four review papers on Professor Fang’s numerous contributions to the fields of experimental design, multivariate analysis, data mining and education. It also contains twenty research articles contributed by prominent and active figures in their fields. The articles cover a wide range of important topics such as experimental design, multivariate analysis, data mining, hypothesis testing and statistical models.