Statistical Methods The Geometric Approach PDF Download
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Author | : David J. Saville |
Publisher | : Springer Science & Business Media |
Total Pages | : 567 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461209714 |
Download Statistical Methods: The Geometric Approach Book in PDF, ePub and Kindle
A novel exposition of the analysis of variance and regression. The key feature here is that these tools are viewed in their natural mathematical setting - the geometry of finite dimensions. This is because geometry clarifies the basic statistics and unifies the many aspects of analysing variance and regression.
Author | : David J. Saville |
Publisher | : CreateSpace |
Total Pages | : 280 |
Release | : 2011-03-20 |
Genre | : Science |
ISBN | : 9781456420420 |
Download Statistical Methods Book in PDF, ePub and Kindle
Are you an applied researcher or a statistics student? If so, have you ever wondered if there is any rhyme or reason behind the apparent jumble of ad hoc statistical “recipes” that are most commonly used by researchers? If you have, then this book is for you! Within its pages, the rhyme and reason are explained in a surprisingly simple, visual and appealing manner. The statistical methods referred to are those based on the “Normal” distribution. They include the paired and independent samples t tests, analysis of variance, and regression. The rhyme is explained by analysing four case studies, one for each of these topics. The key to the rhyme is to use elementary vector geometry. Then the crucial ideas are easily explained by drawing right-angled triangles and applying Pythagoras' Theorem. “Keep it simple” has been our aim. The geometric ideas are first introduced and applied to data sets in two and three dimensions, before we gently introduce higher dimensional examples. Throughout, we use real data sets taken from real research studies, and take care to explain the interpretation of the statistical analyses. In this way, the book integrates the algebraic, numeric, geometric and practical aspects of these basic statistical methods.We hope that many students as well as practicing researchers and statisticians will enjoy this novel visual approach to these ideas.
Author | : Brigitte Le Roux |
Publisher | : Springer Science & Business Media |
Total Pages | : 496 |
Release | : 2004-06-29 |
Genre | : Mathematics |
ISBN | : 9781402022357 |
Download Geometric Data Analysis Book in PDF, ePub and Kindle
Geometric Data Analysis (GDA) is the name suggested by P. Suppes (Stanford University) to designate the approach to Multivariate Statistics initiated by Benzécri as Correspondence Analysis, an approach that has become more and more used and appreciated over the years. This book presents the full formalization of GDA in terms of linear algebra - the most original and far-reaching consequential feature of the approach - and shows also how to integrate the standard statistical tools such as Analysis of Variance, including Bayesian methods. Chapter 9, Research Case Studies, is nearly a book in itself; it presents the methodology in action on three extensive applications, one for medicine, one from political science, and one from education (data borrowed from the Stanford computer-based Educational Program for Gifted Youth ). Thus the readership of the book concerns both mathematicians interested in the applications of mathematics, and researchers willing to master an exceptionally powerful approach of statistical data analysis.
Author | : Shun-ichi Amari |
Publisher | : Springer Science & Business Media |
Total Pages | : 302 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461250560 |
Download Differential-Geometrical Methods in Statistics Book in PDF, ePub and Kindle
From the reviews: "In this Lecture Note volume the author describes his differential-geometric approach to parametrical statistical problems summarizing the results he had published in a series of papers in the last five years. The author provides a geometric framework for a special class of test and estimation procedures for curved exponential families. ... ... The material and ideas presented in this volume are important and it is recommended to everybody interested in the connection between statistics and geometry ..." #Metrika#1 "More than hundred references are given showing the growing interest in differential geometry with respect to statistics. The book can only strongly be recommended to a geodesist since it offers many new insights into statistics on a familiar ground." #Manuscripta Geodaetica#2
Author | : Edmond Saliklis |
Publisher | : Springer |
Total Pages | : 332 |
Release | : 2018-11-07 |
Genre | : Technology & Engineering |
ISBN | : 3319987461 |
Download Structures: A Geometric Approach Book in PDF, ePub and Kindle
Graphic methods for structural design essentially translate problems of algebra into geometric representations, allowing solutions to be reached using geometric construction (ie: drawing pictures) instead of tedious and error-prone arithmetic. This was the common method before the invention of calculators and computers, but had been largely abandoned in the last half century in favor of numerical techniques. However, in recent years the convenience and ease of graphic statics has made a comeback in architecture and engineering. Several professors have begun using graphic statics in the classroom.and.studio environment. But until now, there had been no guidebook that rapidly brings students up to speed on the fundamentals of how to create graphical solutions to statics problems.Graphic Statics introduces all of the traditional graphic statics techniques in a parametric drawing format, using the free program GeoGebra. Then, advanced topics such as indeterminate beams and three dimensional curved surfaces are be covered. Along the way, links to wider design ideas are introduced in a succinct summary of the steps needed to create elegant solutions to many staticequilibrium problems.Meant for students in civil and architectural engineering, architecture,and construction, this practical introduction will also be useful to professionals looking to add the power of graphic statics to their work.
Author | : Thomas D. Wickens |
Publisher | : Psychology Press |
Total Pages | : 216 |
Release | : 2014-02-25 |
Genre | : Psychology |
ISBN | : 1317780221 |
Download The Geometry of Multivariate Statistics Book in PDF, ePub and Kindle
A traditional approach to developing multivariate statistical theory is algebraic. Sets of observations are represented by matrices, linear combinations are formed from these matrices by multiplying them by coefficient matrices, and useful statistics are found by imposing various criteria of optimization on these combinations. Matrix algebra is the vehicle for these calculations. A second approach is computational. Since many users find that they do not need to know the mathematical basis of the techniques as long as they have a way to transform data into results, the computation can be done by a package of computer programs that somebody else has written. An approach from this perspective emphasizes how the computer packages are used, and is usually coupled with rules that allow one to extract the most important numbers from the output and interpret them. Useful as both approaches are--particularly when combined--they can overlook an important aspect of multivariate analysis. To apply it correctly, one needs a way to conceptualize the multivariate relationships that exist among variables. This book is designed to help the reader develop a way of thinking about multivariate statistics, as well as to understand in a broader and more intuitive sense what the procedures do and how their results are interpreted. Presenting important procedures of multivariate statistical theory geometrically, the author hopes that this emphasis on the geometry will give the reader a coherent picture into which all the multivariate techniques fit.
Author | : David J Saville |
Publisher | : |
Total Pages | : 284 |
Release | : 1996-06-01 |
Genre | : |
ISBN | : 9781461207481 |
Download Statistical Methods Book in PDF, ePub and Kindle
Author | : Peter Bühlmann |
Publisher | : Springer Science & Business Media |
Total Pages | : 568 |
Release | : 2011-06-08 |
Genre | : Mathematics |
ISBN | : 364220192X |
Download Statistics for High-Dimensional Data Book in PDF, ePub and Kindle
Modern statistics deals with large and complex data sets, and consequently with models containing a large number of parameters. This book presents a detailed account of recently developed approaches, including the Lasso and versions of it for various models, boosting methods, undirected graphical modeling, and procedures controlling false positive selections. A special characteristic of the book is that it contains comprehensive mathematical theory on high-dimensional statistics combined with methodology, algorithms and illustrations with real data examples. This in-depth approach highlights the methods’ great potential and practical applicability in a variety of settings. As such, it is a valuable resource for researchers, graduate students and experts in statistics, applied mathematics and computer science.
Author | : M.K. Murray |
Publisher | : Routledge |
Total Pages | : 292 |
Release | : 2017-10-19 |
Genre | : Mathematics |
ISBN | : 1351455117 |
Download Differential Geometry and Statistics Book in PDF, ePub and Kindle
Several years ago our statistical friends and relations introduced us to the work of Amari and Barndorff-Nielsen on applications of differential geometry to statistics. This book has arisen because we believe that there is a deep relationship between statistics and differential geometry and moreoever that this relationship uses parts of differential geometry, particularly its 'higher-order' aspects not readily accessible to a statistical audience from the existing literature. It is, in part, a long reply to the frequent requests we have had for references on differential geometry! While we have not gone beyond the path-breaking work of Amari and Barndorff- Nielsen in the realm of applications, our book gives some new explanations of their ideas from a first principles point of view as far as geometry is concerned. In particular it seeks to explain why geometry should enter into parametric statistics, and how the theory of asymptotic expansions involves a form of higher-order differential geometry. The first chapter of the book explores exponential families as flat geometries. Indeed the whole notion of using log-likelihoods amounts to exploiting a particular form of flat space known as an affine geometry, in which straight lines and planes make sense, but lengths and angles are absent. We use these geometric ideas to introduce the notion of the second fundamental form of a family whose vanishing characterises precisely the exponential families.
Author | : D.R. Helsel |
Publisher | : Elsevier |
Total Pages | : 539 |
Release | : 1993-03-03 |
Genre | : Science |
ISBN | : 0080875084 |
Download Statistical Methods in Water Resources Book in PDF, ePub and Kindle
Data on water quality and other environmental issues are being collected at an ever-increasing rate. In the past, however, the techniques used by scientists to interpret this data have not progressed as quickly. This is a book of modern statistical methods for analysis of practical problems in water quality and water resources. The last fifteen years have seen major advances in the fields of exploratory data analysis (EDA) and robust statistical methods. The 'real-life' characteristics of environmental data tend to drive analysis towards the use of these methods. These advances are presented in a practical and relevant format. Alternate methods are compared, highlighting the strengths and weaknesses of each as applied to environmental data. Techniques for trend analysis and dealing with water below the detection limit are topics covered, which are of great interest to consultants in water-quality and hydrology, scientists in state, provincial and federal water resources, and geological survey agencies. The practising water resources scientist will find the worked examples using actual field data from case studies of environmental problems, of real value. Exercises at the end of each chapter enable the mechanics of the methodological process to be fully understood, with data sets included on diskette for easy use. The result is a book that is both up-to-date and immediately relevant to ongoing work in the environmental and water sciences.