Asymptotic Expansions of Integrals

Asymptotic Expansions of Integrals
Author: Norman Bleistein
Publisher: Courier Corporation
Total Pages: 453
Release: 1986-01-01
Genre: Mathematics
ISBN: 0486650820

Excellent introductory text, written by two experts, presents a coherent and systematic view of principles and methods. Topics include integration by parts, Watson's lemma, LaPlace's method, stationary phase, and steepest descents. Additional subjects include the Mellin transform method and less elementary aspects of the method of steepest descents. 1975 edition.

Sequential Analysis and Optimal Design

Sequential Analysis and Optimal Design
Author: Herman Chernoff
Publisher: SIAM
Total Pages: 124
Release: 1972-01-01
Genre: Technology & Engineering
ISBN: 9781611970593

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.

Bayesian Estimation and Experimental Design in Linear Regression Models

Bayesian Estimation and Experimental Design in Linear Regression Models
Author: Jürgen Pilz
Publisher:
Total Pages: 316
Release: 1991-07-09
Genre: Mathematics
ISBN:

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.

Bayesian Statistics for Experimental Scientists

Bayesian Statistics for Experimental Scientists
Author: Richard A. Chechile
Publisher: MIT Press
Total Pages: 473
Release: 2020-09-08
Genre: Mathematics
ISBN: 0262360705

An introduction to the Bayesian approach to statistical inference that demonstrates its superiority to orthodox frequentist statistical analysis. This book offers an introduction to the Bayesian approach to statistical inference, with a focus on nonparametric and distribution-free methods. It covers not only well-developed methods for doing Bayesian statistics but also novel tools that enable Bayesian statistical analyses for cases that previously did not have a full Bayesian solution. The book's premise is that there are fundamental problems with orthodox frequentist statistical analyses that distort the scientific process. Side-by-side comparisons of Bayesian and frequentist methods illustrate the mismatch between the needs of experimental scientists in making inferences from data and the properties of the standard tools of classical statistics.

Optimal Mixture Experiments

Optimal Mixture Experiments
Author: B.K. Sinha
Publisher: Springer
Total Pages: 213
Release: 2014-05-24
Genre: Mathematics
ISBN: 8132217861

​The book dwells mainly on the optimality aspects of mixture designs. As mixture models are a special case of regression models, a general discussion on regression designs has been presented, which includes topics like continuous designs, de la Garza phenomenon, Loewner order domination, Equivalence theorems for different optimality criteria and standard optimality results for single variable polynomial regression and multivariate linear and quadratic regression models. This is followed by a review of the available literature on estimation of parameters in mixture models. Based on recent research findings, the volume also introduces optimal mixture designs for estimation of optimum mixing proportions in different mixture models, which include Scheffé’s quadratic model, Darroch-Waller model, log- contrast model, mixture-amount models, random coefficient models and multi-response model. Robust mixture designs and mixture designs in blocks have been also reviewed. Moreover, some applications of mixture designs in areas like agriculture, pharmaceutics and food and beverages have been presented. Familiarity with the basic concepts of design and analysis of experiments, along with the concept of optimality criteria are desirable prerequisites for a clear understanding of the book. It is likely to be helpful to both theoreticians and practitioners working in the area of mixture experiments.

Optimal Experimental Design with R

Optimal Experimental Design with R
Author: Dieter Rasch
Publisher: CRC Press
Total Pages: 345
Release: 2011-05-18
Genre: Mathematics
ISBN: 1439816980

Experimental design is often overlooked in the literature of applied and mathematical statistics: statistics is taught and understood as merely a collection of methods for analyzing data. Consequently, experimenters seldom think about optimal design, including prerequisites such as the necessary sample size needed for a precise answer for an experi

Theory Of Optimal Experiments

Theory Of Optimal Experiments
Author: V.V. Fedorov
Publisher: Elsevier
Total Pages: 307
Release: 2013-04-20
Genre: Technology & Engineering
ISBN: 0323162460

Theory Of Optimal Experiments

Optimal Design of Experiments

Optimal Design of Experiments
Author: Peter Goos
Publisher: John Wiley & Sons
Total Pages: 249
Release: 2011-06-28
Genre: Science
ISBN: 1119976162

"This is an engaging and informative book on the modern practice of experimental design. The authors' writing style is entertaining, the consulting dialogs are extremely enjoyable, and the technical material is presented brilliantly but not overwhelmingly. The book is a joy to read. Everyone who practices or teaches DOE should read this book." - Douglas C. Montgomery, Regents Professor, Department of Industrial Engineering, Arizona State University "It's been said: 'Design for the experiment, don't experiment for the design.' This book ably demonstrates this notion by showing how tailor-made, optimal designs can be effectively employed to meet a client's actual needs. It should be required reading for anyone interested in using the design of experiments in industrial settings." —Christopher J. Nachtsheim, Frank A Donaldson Chair in Operations Management, Carlson School of Management, University of Minnesota This book demonstrates the utility of the computer-aided optimal design approach using real industrial examples. These examples address questions such as the following: How can I do screening inexpensively if I have dozens of factors to investigate? What can I do if I have day-to-day variability and I can only perform 3 runs a day? How can I do RSM cost effectively if I have categorical factors? How can I design and analyze experiments when there is a factor that can only be changed a few times over the study? How can I include both ingredients in a mixture and processing factors in the same study? How can I design an experiment if there are many factor combinations that are impossible to run? How can I make sure that a time trend due to warming up of equipment does not affect the conclusions from a study? How can I take into account batch information in when designing experiments involving multiple batches? How can I add runs to a botched experiment to resolve ambiguities? While answering these questions the book also shows how to evaluate and compare designs. This allows researchers to make sensible trade-offs between the cost of experimentation and the amount of information they obtain.

The Design and Analysis of Computer Experiments

The Design and Analysis of Computer Experiments
Author: Thomas J. Santner
Publisher: Springer
Total Pages: 446
Release: 2019-01-08
Genre: Mathematics
ISBN: 1493988476

This book describes methods for designing and analyzing experiments that are conducted using a computer code, a computer experiment, and, when possible, a physical experiment. Computer experiments continue to increase in popularity as surrogates for and adjuncts to physical experiments. Since the publication of the first edition, there have been many methodological advances and software developments to implement these new methodologies. The computer experiments literature has emphasized the construction of algorithms for various data analysis tasks (design construction, prediction, sensitivity analysis, calibration among others), and the development of web-based repositories of designs for immediate application. While it is written at a level that is accessible to readers with Masters-level training in Statistics, the book is written in sufficient detail to be useful for practitioners and researchers. New to this revised and expanded edition: • An expanded presentation of basic material on computer experiments and Gaussian processes with additional simulations and examples • A new comparison of plug-in prediction methodologies for real-valued simulator output • An enlarged discussion of space-filling designs including Latin Hypercube designs (LHDs), near-orthogonal designs, and nonrectangular regions • A chapter length description of process-based designs for optimization, to improve good overall fit, quantile estimation, and Pareto optimization • A new chapter describing graphical and numerical sensitivity analysis tools • Substantial new material on calibration-based prediction and inference for calibration parameters • Lists of software that can be used to fit models discussed in the book to aid practitioners

Bayesian Statistics, A Review

Bayesian Statistics, A Review
Author: D. V. Lindley
Publisher: SIAM
Total Pages: 88
Release: 1972-01-31
Genre: Mathematics
ISBN: 9781611970654

A study of those statistical ideas that use a probability distribution over parameter space. The first part describes the axiomatic basis in the concept of coherence and the implications of this for sampling theory statistics. The second part discusses the use of Bayesian ideas in many branches of statistics.