A Bayesian Approach To The Design And Analysis Of Experiments For Regression Models

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A Bayesian Approach to the Design and Analysis of Experiments for Regression Models

Author : Salvatore J. Monaco
Publisher :
ISBN 13 :
Total Pages : 111 pages
Book Rating : 4.:/5 (122 download)

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Book Synopsis A Bayesian Approach to the Design and Analysis of Experiments for Regression Models by : Salvatore J. Monaco

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).

Bayesian Estimation and Experimental Design in Linear Regression Models

Author : Jürgen Pilz
Publisher :
ISBN 13 :
Total Pages : 316 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Bayesian Estimation and Experimental Design in Linear Regression Models by : Jürgen Pilz

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.

Handbook of Design and Analysis of Experiments

Author : Angela Dean
Publisher : CRC Press
ISBN 13 : 146650434X
Total Pages : 946 pages
Book Rating : 4.4/5 (665 download)

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Book Synopsis Handbook of Design and Analysis of Experiments by : Angela Dean

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.

Bayesian Analysis of Linear Models

Author : Broemeling
Publisher : CRC Press
ISBN 13 : 1351464485
Total Pages : 472 pages
Book Rating : 4.3/5 (514 download)

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Book Synopsis Bayesian Analysis of Linear Models by : Broemeling

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.

Bayesian Statistical Methods

Author : Brian J. Reich
Publisher : CRC Press
ISBN 13 : 0429514344
Total Pages : 197 pages
Book Rating : 4.4/5 (295 download)

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Book Synopsis Bayesian Statistical Methods by : Brian J. Reich

Download or read book Bayesian Statistical Methods written by Brian J. Reich and published by CRC Press. This book was released on 2019-04-12 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayesian Statistical Methods provides data scientists with the foundational and computational tools needed to carry out a Bayesian analysis. This book focuses on Bayesian methods applied routinely in practice including multiple linear regression, mixed effects models and generalized linear models (GLM). The authors include many examples with complete R code and comparisons with analogous frequentist procedures. In addition to the basic concepts of Bayesian inferential methods, the book covers many general topics: Advice on selecting prior distributions Computational methods including Markov chain Monte Carlo (MCMC) Model-comparison and goodness-of-fit measures, including sensitivity to priors Frequentist properties of Bayesian methods Case studies covering advanced topics illustrate the flexibility of the Bayesian approach: Semiparametric regression Handling of missing data using predictive distributions Priors for high-dimensional regression models Computational techniques for large datasets Spatial data analysis The advanced topics are presented with sufficient conceptual depth that the reader will be able to carry out such analysis and argue the relative merits of Bayesian and classical methods. A repository of R code, motivating data sets, and complete data analyses are available on the book’s website. Brian J. Reich, Associate Professor of Statistics at North Carolina State University, is currently the editor-in-chief of the Journal of Agricultural, Biological, and Environmental Statistics and was awarded the LeRoy & Elva Martin Teaching Award. Sujit K. Ghosh, Professor of Statistics at North Carolina State University, has over 22 years of research and teaching experience in conducting Bayesian analyses, received the Cavell Brownie mentoring award, and served as the Deputy Director at the Statistical and Applied Mathematical Sciences Institute.

Design and Analysis of Experiments, Volume 3

Author : Klaus Hinkelmann
Publisher : John Wiley & Sons
ISBN 13 : 0470530685
Total Pages : 598 pages
Book Rating : 4.4/5 (75 download)

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Book Synopsis Design and Analysis of Experiments, Volume 3 by : Klaus Hinkelmann

Download or read book Design and Analysis of Experiments, Volume 3 written by Klaus Hinkelmann and published by John Wiley & Sons. This book was released on 2012-02-14 with total page 598 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides timely applications, modifications, and extensions of experimental designs for a variety of disciplines Design and Analysis of Experiments, Volume 3: Special Designs and Applications continues building upon the philosophical foundations of experimental design by providing important, modern applications of experimental design to the many fields that utilize them. The book also presents optimal and efficient designs for practice and covers key topics in current statistical research. Featuring contributions from leading researchers and academics, the book demonstrates how the presented concepts are used across various fields from genetics and medicinal and pharmaceutical research to manufacturing, engineering, and national security. Each chapter includes an introduction followed by the historical background as well as in-depth procedures that aid in the construction and analysis of the discussed designs. Topical coverage includes: Genetic cross experiments, microarray experiments, and variety trials Clinical trials, group-sequential designs, and adaptive designs Fractional factorial and search, choice, and optimal designs for generalized linear models Computer experiments with applications to homeland security Robust parameter designs and split-plot type response surface designs Analysis of directional data experiments Throughout the book, illustrative and numerical examples utilize SAS®, JMP®, and R software programs to demonstrate the discussed techniques. Related data sets and software applications are available on the book's related FTP site. Design and Analysis of Experiments, Volume 3 is an ideal textbook for graduate courses in experimental design and also serves as a practical, hands-on reference for statisticians and researchers across a wide array of subject areas, including biological sciences, engineering, medicine, and business.

Bayesian Analysis in Statistics and Econometrics

Author : Donald A. Berry
Publisher : John Wiley & Sons
ISBN 13 : 9780471118565
Total Pages : 610 pages
Book Rating : 4.1/5 (185 download)

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Book Synopsis Bayesian Analysis in Statistics and Econometrics by : Donald A. Berry

Download or read book Bayesian Analysis in Statistics and Econometrics written by Donald A. Berry and published by John Wiley & Sons. This book was released on 1996 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a definitive work that captures the current state of knowledge of Bayesian Analysis in Statistics and Econometrics and attempts to move it forward. It covers such topics as foundations, forecasting inferential matters, regression, computation and applications.

A Bayesian Approach to the Design and Analysis of Computer Experiments

Author :
Publisher :
ISBN 13 :
Total Pages : 5 pages
Book Rating : 4.:/5 (871 download)

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Book Synopsis A Bayesian Approach to the Design and Analysis of Computer Experiments by :

Download or read book A Bayesian Approach to the Design and Analysis of Computer Experiments written by and published by . This book was released on 1988 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Bayesian Data Analysis

Author : Andrew Gelman
Publisher : CRC Press
ISBN 13 : 1439898200
Total Pages : 663 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis Bayesian Data Analysis by : Andrew Gelman

Download or read book Bayesian Data Analysis written by Andrew Gelman and published by CRC Press. This book was released on 2013-11-27 with total page 663 pages. Available in PDF, EPUB and Kindle. Book excerpt: Winner of the 2016 De Groot Prize from the International Society for Bayesian AnalysisNow 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

Bayesian Reliability

Author : Michael S. Hamada
Publisher : Springer Science & Business Media
ISBN 13 : 0387779507
Total Pages : 445 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis Bayesian Reliability by : Michael S. Hamada

Download or read book Bayesian Reliability written by Michael S. Hamada and published by Springer Science & Business Media. This book was released on 2008-08-15 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayesian Reliability presents modern methods and techniques for analyzing reliability data from a Bayesian perspective. The adoption and application of Bayesian methods in virtually all branches of science and engineering have significantly increased over the past few decades. This increase is largely due to advances in simulation-based computational tools for implementing Bayesian methods. The authors extensively use such tools throughout this book, focusing on assessing the reliability of components and systems with particular attention to hierarchical models and models incorporating explanatory variables. Such models include failure time regression models, accelerated testing models, and degradation models. The authors pay special attention to Bayesian goodness-of-fit testing, model validation, reliability test design, and assurance test planning. Throughout the book, the authors use Markov chain Monte Carlo (MCMC) algorithms for implementing Bayesian analyses -- algorithms that make the Bayesian approach to reliability computationally feasible and conceptually straightforward. This book is primarily a reference collection of modern Bayesian methods in reliability for use by reliability practitioners. There are more than 70 illustrative examples, most of which utilize real-world data. This book can also be used as a textbook for a course in reliability and contains more than 160 exercises. Noteworthy highlights of the book include Bayesian approaches for the following: Goodness-of-fit and model selection methods Hierarchical models for reliability estimation Fault tree analysis methodology that supports data acquisition at all levels in the tree Bayesian networks in reliability analysis Analysis of failure count and failure time data collected from repairable systems, and the assessment of various related performance criteria Analysis of nondestructive and destructive degradation data Optimal design of reliability experiments Hierarchical reliability assurance testing

Design and Analysis of Experiments

Author : Douglas C. Montgomery
Publisher : John Wiley & Sons
ISBN 13 : 1119113474
Total Pages : 752 pages
Book Rating : 4.1/5 (191 download)

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Book Synopsis Design and Analysis of Experiments by : Douglas C. Montgomery

Download or read book Design and Analysis of Experiments written by Douglas C. Montgomery and published by John Wiley & Sons. This book was released on 2017 with total page 752 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The eighth edition of Design and Analysis of Experiments continues to provide extensive and in-depth information on engineering, business, and statistics-as well as informative ways to help readers design and analyze experiments for improving the quality, efficiency and performance of working systems. Furthermore, the text maintains its comprehensive coverage by including: new examples, exercises, and problems (including in the areas of biochemistry and biotechnology); new topics and problems in the area of response surface; new topics in nested and split-plot design; and the residual maximum likelihood method is now emphasized throughout the book"--

Design and Analysis of Experiments with R

Author : John Lawson
Publisher : CRC Press
ISBN 13 : 1498728480
Total Pages : 629 pages
Book Rating : 4.4/5 (987 download)

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Book Synopsis Design and Analysis of Experiments with R by : John Lawson

Download or read book Design and Analysis of Experiments with R written by John Lawson and published by CRC Press. This book was released on 2014-12-17 with total page 629 pages. Available in PDF, EPUB and Kindle. Book excerpt: Design and Analysis of Experiments with R presents a unified treatment of experimental designs and design concepts commonly used in practice. It connects the objectives of research to the type of experimental design required, describes the process of creating the design and collecting the data, shows how to perform the proper analysis of the data,

Regression Modelling wih Spatial and Spatial-Temporal Data

Author : Robert P. Haining
Publisher : CRC Press
ISBN 13 : 0429529104
Total Pages : 527 pages
Book Rating : 4.4/5 (295 download)

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Book Synopsis Regression Modelling wih Spatial and Spatial-Temporal Data by : Robert P. Haining

Download or read book Regression Modelling wih Spatial and Spatial-Temporal Data written by Robert P. Haining and published by CRC Press. This book was released on 2020-01-27 with total page 527 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modelling Spatial and Spatial-Temporal Data: A Bayesian Approach is aimed at statisticians and quantitative social, economic and public health students and researchers who work with spatial and spatial-temporal data. It assumes a grounding in statistical theory up to the standard linear regression model. The book compares both hierarchical and spatial econometric modelling, providing both a reference and a teaching text with exercises in each chapter. The book provides a fully Bayesian, self-contained, treatment of the underlying statistical theory, with chapters dedicated to substantive applications. The book includes WinBUGS code and R code and all datasets are available online. Part I covers fundamental issues arising when modelling spatial and spatial-temporal data. Part II focuses on modelling cross-sectional spatial data and begins by describing exploratory methods that help guide the modelling process. There are then two theoretical chapters on Bayesian models and a chapter of applications. Two chapters follow on spatial econometric modelling, one describing different models, the other substantive applications. Part III discusses modelling spatial-temporal data, first introducing models for time series data. Exploratory methods for detecting different types of space-time interaction are presented followed by two chapters on the theory of space-time separable (without space-time interaction) and inseparable (with space-time interaction) models. An applications chapter includes: the evaluation of a policy intervention; analysing the temporal dynamics of crime hotspots; chronic disease surveillance; and testing for evidence of spatial spillovers in the spread of an infectious disease. A final chapter suggests some future directions and challenges.

Bayesian and Frequentist Regression Methods

Author : Jon Wakefield
Publisher : Springer Science & Business Media
ISBN 13 : 1441909257
Total Pages : 700 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Bayesian and Frequentist Regression Methods by : Jon Wakefield

Download or read book Bayesian and Frequentist Regression Methods written by Jon Wakefield and published by Springer Science & Business Media. This book was released on 2013-01-04 with total page 700 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayesian and Frequentist Regression Methods provides a modern account of both Bayesian and frequentist methods of regression analysis. Many texts cover one or the other of the approaches, but this is the most comprehensive combination of Bayesian and frequentist methods that exists in one place. The two philosophical approaches to regression methodology are featured here as complementary techniques, with theory and data analysis providing supplementary components of the discussion. In particular, methods are illustrated using a variety of data sets. The majority of the data sets are drawn from biostatistics but the techniques are generalizable to a wide range of other disciplines.

Bayesian Inference in Statistical Analysis

Author : George E. P. Box
Publisher : John Wiley & Sons
ISBN 13 : 111803144X
Total Pages : 610 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis Bayesian Inference in Statistical Analysis by : George E. P. Box

Download or read book Bayesian Inference in Statistical Analysis written by George E. P. Box and published by John Wiley & Sons. This book was released on 2011-01-25 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: Its main objective is to examine the application and relevance of Bayes' theorem to problems that arise in scientific investigation in which inferences must be made regarding parameter values about which little is known a priori. Begins with a discussion of some important general aspects of the Bayesian approach such as the choice of prior distribution, particularly noninformative prior distribution, the problem of nuisance parameters and the role of sufficient statistics, followed by many standard problems concerned with the comparison of location and scale parameters. The main thrust is an investigation of questions with appropriate analysis of mathematical results which are illustrated with numerical examples, providing evidence of the value of the Bayesian approach.

Contributions to the Analysis of Experiments Using Empirical Bayes Techniques

Author : James Dillon Delaney
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (713 download)

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Book Synopsis Contributions to the Analysis of Experiments Using Empirical Bayes Techniques by : James Dillon Delaney

Download or read book Contributions to the Analysis of Experiments Using Empirical Bayes Techniques written by James Dillon Delaney and published by . This book was released on 2006 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Specifying a prior distribution for the large number of parameters in the linear statistical model is a difficult step in the Bayesian approach to the design and analysis of experiments. Here we address this difficulty by proposing the use of functional priors and then by working out important details for three and higher level experiments. One of the challenges presented by higher level experiments is that a factor can be either qualitative or quantitative. We propose appropriate correlation functions and coding schemes so that the prior distribution is simple and the results easily interpretable. The prior incorporates well known experimental design principles such as effect hierarchy and effect heredity, which helps to automatically resolve the aliasing problems experienced in fractional designs. The second part of the thesis focuses on the analysis of optimization experiments. Not uncommon are designed experiments with their primary purpose being to determine optimal settings for all of the factors in some predetermined set. Here we distinguish between the two concepts of statistical significance and practical significance. We perform estimation via an empirical Bayes data analysis methodology that has been detailed in the recent literature. But then propose an alternative to the usual next step in determining optimal factor level settings. Instead of implementing variable or model selection techniques, we propose an objective function that assists in our goal of finding the ideal settings for all factors over which we experimented. The usefulness of the new approach is illustrated through the analysis of some real experiments as well as simulation.

Frontiers of Statistical Decision Making and Bayesian Analysis

Author : Ming-Hui Chen
Publisher : Springer Science & Business Media
ISBN 13 : 1441969446
Total Pages : 631 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Frontiers of Statistical Decision Making and Bayesian Analysis by : Ming-Hui Chen

Download or read book Frontiers of Statistical Decision Making and Bayesian Analysis written by Ming-Hui Chen and published by Springer Science & Business Media. This book was released on 2010-07-24 with total page 631 pages. Available in PDF, EPUB and Kindle. Book excerpt: Research in Bayesian analysis and statistical decision theory is rapidly expanding and diversifying, making it increasingly more difficult for any single researcher to stay up to date on all current research frontiers. This book provides a review of current research challenges and opportunities. While the book can not exhaustively cover all current research areas, it does include some exemplary discussion of most research frontiers. Topics include objective Bayesian inference, shrinkage estimation and other decision based estimation, model selection and testing, nonparametric Bayes, the interface of Bayesian and frequentist inference, data mining and machine learning, methods for categorical and spatio-temporal data analysis and posterior simulation methods. Several major application areas are covered: computer models, Bayesian clinical trial design, epidemiology, phylogenetics, bioinformatics, climate modeling and applications in political science, finance and marketing. As a review of current research in Bayesian analysis the book presents a balance between theory and applications. The lack of a clear demarcation between theoretical and applied research is a reflection of the highly interdisciplinary and often applied nature of research in Bayesian statistics. The book is intended as an update for researchers in Bayesian statistics, including non-statisticians who make use of Bayesian inference to address substantive research questions in other fields. It would also be useful for graduate students and research scholars in statistics or biostatistics who wish to acquaint themselves with current research frontiers.