Theory of the Combination of Observations Least Subject to Error PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Theory of the Combination of Observations Least Subject to Error PDF full book. Access full book title Theory of the Combination of Observations Least Subject to Error by Carl Friedrich Gauss. Download full books in PDF and EPUB format.
Author: Carl Friedrich Gauss
Publisher: SIAM
ISBN: 9781611971248
Category : Mathematics
Languages : en
Pages : 252
Get Book Here
Book Description
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
ISBN: 9781611971248
Category : Mathematics
Languages : en
Pages : 252
Get Book Here
Book Description
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
ISBN: 9780898713473
Category : Mathematics
Languages : en
Pages : 260
Get Book Here
Book Description
English translation of Gauss' two memoirs which contain his final, definitive treatment of least squares and wealth of additional material.
Author: Steven J. Osterlind
Publisher: Oxford University Press
ISBN: 0192567381
Category : Science
Languages : en
Pages : 352
Get Book Here
Book Description
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
ISBN: 1134340451
Category : Business & Economics
Languages : en
Pages : 409
Get Book Here
Book Description
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: Bernhard Schipp
Publisher: Springer Science & Business Media
ISBN: 3790821217
Category : Mathematics
Languages : en
Pages : 438
Get Book Here
Book Description
This Festschrift is dedicated to Götz Trenkler on the occasion of his 65th birthday. As can be seen from the long list of contributions, Götz has had and still has an enormous range of interests, and colleagues to share these interests with. He is a leading expert in linear models with a particular focus on matrix algebra in its relation to statistics. He has published in almost all major statistics and matrix theory journals. His research activities also include other areas (like nonparametrics, statistics and sports, combination of forecasts and magic squares, just to mention afew). Götz Trenkler was born in Dresden in 1943. After his school years in East G- many and West-Berlin, he obtained a Diploma in Mathematics from Free University of Berlin (1970), where he also discovered his interest in Mathematical Statistics. In 1973, he completed his Ph.D. with a thesis titled: On a distance-generating fu- tion of probability measures. He then moved on to the University of Hannover to become Lecturer and to write a habilitation-thesis (submitted 1979) on alternatives to the Ordinary Least Squares estimator in the Linear Regression Model, a topic that would become his predominant ?eld of research in the years to come.
Author: Prakash Gorroochurn
Publisher: John Wiley & Sons
ISBN: 1119127920
Category : Mathematics
Languages : en
Pages : 776
Get Book Here
Book Description
"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: Ake Bjorck
Publisher: SIAM
ISBN: 9781611971484
Category : Mathematics
Languages : en
Pages : 425
Get Book Here
Book Description
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: Ali H. Sayed
Publisher: Cambridge University Press
ISBN: 1009218255
Category : Technology & Engineering
Languages : en
Pages : 1166
Get Book Here
Book Description
This extraordinary three-volume work, written in an engaging and rigorous style by a world authority in the field, provides an accessible, comprehensive introduction to the full spectrum of mathematical and statistical techniques underpinning contemporary methods in data-driven learning and inference. This second volume, Inference, builds on the foundational topics established in volume I to introduce students to techniques for inferring unknown variables and quantities, including Bayesian inference, Monte Carlo Markov Chain methods, maximum-likelihood estimation, hidden Markov models, Bayesian networks, and reinforcement learning. A consistent structure and pedagogy is employed throughout this volume to reinforce student understanding, with over 350 end-of-chapter problems (including solutions for instructors), 180 solved examples, almost 200 figures, datasets and downloadable Matlab code. Supported by sister volumes Foundations and Learning, and unique in its scale and depth, this textbook sequence is ideal for early-career researchers and graduate students across many courses in signal processing, machine learning, statistical analysis, data science and inference.
Author: Bill Triggs
Publisher: Springer
ISBN: 3540444807
Category : Computers
Languages : en
Pages : 394
Get Book Here
Book Description
This book constitutes the thoroughly refereed post-workshop proceedings of the International Workshop on Vision Algorithms held in Corfu, Greece in September 1999 in conjunction with ICCV'99. The 15 revised full papers presented were carefully reviewed and selected from 65 submissions; each paper is complemented by a brief transcription of the discussion that followed its presentation. Also included are two invited contributions and two expert reviews as well as a panel discussion. The volume spans the whole range of algorithms for geometric vision. The authors and volume editors succeeded in providing added value beyond a mere collection of papers and made the volume a state-of-the-art survey of their field.
Author: Marcel Boumans
Publisher: Oxford University Press
ISBN: 019938830X
Category : Business & Economics
Languages : en
Pages : 213
Get Book Here
Book Description
The conduct of most of social science occurs outside the laboratory. Such studies in field science explore phenomena that cannot for practical, technical, or ethical reasons be explored under controlled conditions. These phenomena cannot be fully isolated from their environment or investigated by manipulation or intervention. Yet measurement, including rigorous or clinical measurement, does provide analysts with a sound basis for discerning what occurs under field conditions, and why. In Science Outside the Laboratory, Marcel Boumans explores the state of measurement theory, its reliability, and the role expert judgment plays in field investigations from the perspective of the philosophy of science. Its discussion of the problems of passive observation, the calculus of observation, the two-model problem, and model-based consensus uses illustrations drawn primarily from economics. Rich in research and discussion, the volume clarifies the extent to which measurement provides valid information about objects and events in field sciences, but also has implications for measurement in the laboratory. Scholars in the fields of philosophy of science, social science, and economics will find Science Outside the Laboratory a compelling and informative read.
