Theory Of The Combination Of Observations Least Subject To Error
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| Author | : Carl Friedrich Gauss |
| Publisher | : SIAM |
| Total Pages | : 252 |
| Release | : 1995-01-01 |
| Genre | : Mathematics |
| ISBN | : 9781611971248 |
In the 1820s Gauss published two memoirs on least squares, which contain his final, definitive treatment of the area along with a wealth of material on probability, statistics, numerical analysis, and geodesy. These memoirs, originally published in Latin with German Notices, have been inaccessible to the English-speaking community. Here for the first time they are collected in an English translation. For scholars interested in comparisons the book includes the original text and the English translation on facing pages. More generally the book will be of interest to statisticians, numerical analysts, and other scientists who are interested in what Gauss did and how he set about doing it. An Afterword by the translator, G. W. Stewart, places Gauss's contributions in historical perspective.
| Author | : Carl Friedrich Gauss |
| Publisher | : SIAM |
| Total Pages | : 260 |
| Release | : 1995-01-01 |
| Genre | : Mathematics |
| ISBN | : 9780898713473 |
English translation of Gauss' two memoirs which contain his final, definitive treatment of least squares and wealth of additional material.
| Author | : M.J.T. Milton |
| Publisher | : IOS Press |
| Total Pages | : 480 |
| Release | : 2021-12-22 |
| Genre | : Science |
| ISBN | : 1643682474 |
The use of standard and reliable measurements is essential in many areas of life, but nowhere is it of more crucial importance than in the world of science, and physics in particular. This book contains 20 contributions presented as part of Course 206 of the International School of Physics Enrico Fermi on New Frontiers for Metrology: From Biology and Chemistry to Quantum and Data Science, held in Varenna, Italy, from 4 -13 July 2019. The Course was the 7th in the Enrico Fermi series devoted to metrology, and followed a milestone in the history of measurement: the adoption of new definitions for the base units of the SI. During the Course, participants reviewed the decision and discussed how the new foundation for metrology is opening new possibilities for physics, with several of the lecturers reflecting on the implications for an easier exploration of the unification of quantum mechanics and gravity. A wide range of other topics were covered, from measuring color and appearance to atomic weights and radiation, and including the application of metrological principles to the management and interpretation of very large sets of scientific data and the application of metrology to biology. The book also contains a selection of posters from the best of those presented by students at the Course. Offering a fascinating exploration of the latest thinking on the subject of metrology, this book will be of interest to researchers and practitioners from many fields.
| Author | : Ali H. Sayed |
| Publisher | : Cambridge University Press |
| Total Pages | : 1165 |
| Release | : 2022-11-30 |
| Genre | : Computers |
| ISBN | : 1009218263 |
Discover techniques for inferring unknown variables and quantities with the second volume of this extraordinary three-volume set.
| Author | : Steven J. Osterlind |
| Publisher | : Oxford University Press |
| Total Pages | : 352 |
| Release | : 2019-01-24 |
| Genre | : Science |
| ISBN | : 0192567381 |
Quantitative thinking is our inclination to view natural and everyday phenomena through a lens of measurable events, with forecasts, odds, predictions, and likelihood playing a dominant part. The Error of Truth recounts the astonishing and unexpected tale of how quantitative thinking came to be, and its rise to primacy in the nineteenth and early twentieth centuries. Additionally, it considers how seeing the world through a quantitative lens has shaped our perception of the world we live in, and explores the lives of the individuals behind its early establishment. This worldview was unlike anything humankind had before, and it came about because of a momentous human achievement: we had learned how to measure uncertainty. Probability as a science was conceptualised. As a result of probability theory, we now had correlations, reliable predictions, regressions, the bellshaped curve for studying social phenomena, and the psychometrics of educational testing. Significantly, these developments happened during a relatively short period in world history— roughly, the 130-year period from 1790 to 1920, from about the close of the Napoleonic era, through the Enlightenment and the Industrial Revolutions, to the end of World War I. At which time, transportation had advanced rapidly, due to the invention of the steam engine, and literacy rates had increased exponentially. This brief period in time was ready for fresh intellectual activity, and it gave a kind of impetus for the probability inventions. Quantification is now everywhere in our daily lives, such as in the ubiquitous microchip in smartphones, cars, and appliances; in the Bayesian logic of artificial intelligence, as well as applications in business, engineering, medicine, economics, and elsewhere. Probability is the foundation of quantitative thinking. The Error of Truth tells its story— when, why, and how it happened.
| Author | : John Chipman |
| Publisher | : Routledge |
| Total Pages | : 409 |
| Release | : 2013-03-01 |
| Genre | : Business & Economics |
| ISBN | : 1134340451 |
When learning econometrics, what better way than to be taught by one of its masters. In this significant new volume, John Chipman, the eminence grise of econometrics, presents his classic lectures in econometric theory. Starting with the linear regression model, least squares, Gauss-Markov theory and the first principals of econometrics, this book guides the introductory student to an advanced stage of ability. The text covers multicollinearity and reduced-rank estimation, the treatment of linear restrictions and minimax estimation. Also included are chapters on the autocorrelation of residuals and simultaneous-equation estimation. By the end of the text, students will have a solid grounding in econometrics. Despite the frequent complexity of the subject matter, Chipman's clear explanations, concise prose and sharp analysis make this book stand out from others in the field. With mathematical rigor sharpened by a lifetime of econometric analysis, this significant volume is sure to become a seminal and indispensable text in this area.
| Author | : Prakash Gorroochurn |
| Publisher | : John Wiley & Sons |
| Total Pages | : 776 |
| Release | : 2016-04-04 |
| Genre | : Mathematics |
| ISBN | : 1119127920 |
"There is nothing like it on the market...no others are as encyclopedic...the writing is exemplary: simple, direct, and competent." —George W. Cobb, Professor Emeritus of Mathematics and Statistics, Mount Holyoke College Written in a direct and clear manner, Classic Topics on the History of Modern Mathematical Statistics: From Laplace to More Recent Times presents a comprehensive guide to the history of mathematical statistics and details the major results and crucial developments over a 200-year period. Presented in chronological order, the book features an account of the classical and modern works that are essential to understanding the applications of mathematical statistics. Divided into three parts, the book begins with extensive coverage of the probabilistic works of Laplace, who laid much of the foundations of later developments in statistical theory. Subsequently, the second part introduces 20th century statistical developments including work from Karl Pearson, Student, Fisher, and Neyman. Lastly, the author addresses post-Fisherian developments. Classic Topics on the History of Modern Mathematical Statistics: From Laplace to More Recent Times also features: A detailed account of Galton's discovery of regression and correlation as well as the subsequent development of Karl Pearson's X2 and Student's t A comprehensive treatment of the permeating influence of Fisher in all aspects of modern statistics beginning with his work in 1912 Significant coverage of Neyman–Pearson theory, which includes a discussion of the differences to Fisher’s works Discussions on key historical developments as well as the various disagreements, contrasting information, and alternative theories in the history of modern mathematical statistics in an effort to provide a thorough historical treatment Classic Topics on the History of Modern Mathematical Statistics: From Laplace to More Recent Times is an excellent reference for academicians with a mathematical background who are teaching or studying the history or philosophical controversies of mathematics and statistics. The book is also a useful guide for readers with a general interest in statistical inference.
| Author | : Erik Grafarend |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 1026 |
| Release | : 2012-08-15 |
| Genre | : Science |
| ISBN | : 3642222412 |
Here we present a nearly complete treatment of the Grand Universe of linear and weakly nonlinear regression models within the first 8 chapters. Our point of view is both an algebraic view as well as a stochastic one. For example, there is an equivalent lemma between a best, linear uniformly unbiased estimation (BLUUE) in a Gauss-Markov model and a least squares solution (LESS) in a system of linear equations. While BLUUE is a stochastic regression model, LESS is an algebraic solution. In the first six chapters we concentrate on underdetermined and overdeterimined linear systems as well as systems with a datum defect. We review estimators/algebraic solutions of type MINOLESS, BLIMBE, BLUMBE, BLUUE, BIQUE, BLE, BIQUE and Total Least Squares. The highlight is the simultaneous determination of the first moment and the second central moment of a probability distribution in an inhomogeneous multilinear estimation by the so called E-D correspondence as well as its Bayes design. In addition, we discuss continuous networks versus discrete networks, use of Grassmann-Pluecker coordinates, criterion matrices of type Taylor-Karman as well as FUZZY sets. Chapter seven is a speciality in the treatment of an overdetermined system of nonlinear equations on curved manifolds. The von Mises-Fisher distribution is characteristic for circular or (hyper) spherical data. Our last chapter eight is devoted to probabilistic regression, the special Gauss-Markov model with random effects leading to estimators of type BLIP and VIP including Bayesian estimation. A great part of the work is presented in four Appendices. Appendix A is a treatment, of tensor algebra, namely linear algebra, matrix algebra and multilinear algebra. Appendix B is devoted to sampling distributions and their use in terms of confidence intervals and confidence regions. Appendix C reviews the elementary notions of statistics, namely random events and stochastic processes. Appendix D introduces the basics of Groebner basis algebra, its careful definition, the Buchberger Algorithm, especially the C. F. Gauss combinatorial algorithm.
| Author | : Ake Bjorck |
| Publisher | : SIAM |
| Total Pages | : 425 |
| Release | : 1996-01-01 |
| Genre | : Mathematics |
| ISBN | : 9781611971484 |
The method of least squares was discovered by Gauss in 1795. It has since become the principal tool to reduce the influence of errors when fitting models to given observations. Today, applications of least squares arise in a great number of scientific areas, such as statistics, geodetics, signal processing, and control. In the last 20 years there has been a great increase in the capacity for automatic data capturing and computing. Least squares problems of large size are now routinely solved. Tremendous progress has been made in numerical methods for least squares problems, in particular for generalized and modified least squares problems and direct and iterative methods for sparse problems. Until now there has not been a monograph that covers the full spectrum of relevant problems and methods in least squares. This volume gives an in-depth treatment of topics such as methods for sparse least squares problems, iterative methods, modified least squares, weighted problems, and constrained and regularized problems. The more than 800 references provide a comprehensive survey of the available literature on the subject.
| Author | : Warren E. Stewart |
| Publisher | : John Wiley & Sons |
| Total Pages | : 288 |
| Release | : 2008-03-17 |
| Genre | : Science |
| ISBN | : 0470282029 |
Learn to apply modeling and parameter estimation tools and strategies to chemicalprocesses using your personal computer This book introduces readers to powerful parameter estimation and computational methods for modeling complex chemical reactions and reaction processes. It presents useful mathematical models, numerical methods for solving them, and statistical methods for testing and discriminating candidate models with experimental data. Topics covered include: Chemical reaction models Chemical reactor models Probability and statistics Bayesian estimation Process modeling with single-response data Process modeling with multi-response data Computer software (Athena Visual Studio) is available via a related Web site http://www.athenavisual.com enabling readers to carry out parameter estimation based on their data and to carry out process modeling using these parameters. As an aid to the reader, an appendix of example problems and solutions is provided. Computer-Aided Modeling of Reactive Systems is an ideal supplemental text for advanced undergraduates and graduate students in chemical engineering courses, while it also serves as a valuable resource for practitioners in industry who want to keep up to date on the most current tools and strategies available.
