Lectures On Algebraic Statistics PDF Download
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Author | : Mathias Drton |
Publisher | : Springer Science & Business Media |
Total Pages | : 177 |
Release | : 2009-04-25 |
Genre | : Mathematics |
ISBN | : 3764389052 |
Download Lectures on Algebraic Statistics Book in PDF, ePub and Kindle
How does an algebraic geometer studying secant varieties further the understanding of hypothesis tests in statistics? Why would a statistician working on factor analysis raise open problems about determinantal varieties? Connections of this type are at the heart of the new field of "algebraic statistics". In this field, mathematicians and statisticians come together to solve statistical inference problems using concepts from algebraic geometry as well as related computational and combinatorial techniques. The goal of these lectures is to introduce newcomers from the different camps to algebraic statistics. The introduction will be centered around the following three observations: many important statistical models correspond to algebraic or semi-algebraic sets of parameters; the geometry of these parameter spaces determines the behaviour of widely used statistical inference procedures; computational algebraic geometry can be used to study parameter spaces and other features of statistical models.
Author | : Seth Sullivant |
Publisher | : American Mathematical Society |
Total Pages | : 506 |
Release | : 2023-11-17 |
Genre | : Mathematics |
ISBN | : 1470475103 |
Download Algebraic Statistics Book in PDF, ePub and Kindle
Algebraic statistics uses tools from algebraic geometry, commutative algebra, combinatorics, and their computational sides to address problems in statistics and its applications. The starting point for this connection is the observation that many statistical models are semialgebraic sets. The algebra/statistics connection is now over twenty years old, and this book presents the first broad introductory treatment of the subject. Along with background material in probability, algebra, and statistics, this book covers a range of topics in algebraic statistics including algebraic exponential families, likelihood inference, Fisher's exact test, bounds on entries of contingency tables, design of experiments, identifiability of hidden variable models, phylogenetic models, and model selection. With numerous examples, references, and over 150 exercises, this book is suitable for both classroom use and independent study.
Author | : Günter Harder |
Publisher | : Springer Science & Business Media |
Total Pages | : 301 |
Release | : 2008-08-01 |
Genre | : Mathematics |
ISBN | : 3834895016 |
Download Lectures on Algebraic Geometry I Book in PDF, ePub and Kindle
This book and the following second volume is an introduction into modern algebraic geometry. In the first volume the methods of homological algebra, theory of sheaves, and sheaf cohomology are developed. These methods are indispensable for modern algebraic geometry, but they are also fundamental for other branches of mathematics and of great interest in their own. In the last chapter of volume I these concepts are applied to the theory of compact Riemann surfaces. In this chapter the author makes clear how influential the ideas of Abel, Riemann and Jacobi were and that many of the modern methods have been anticipated by them.
Author | : L. Pachter |
Publisher | : Cambridge University Press |
Total Pages | : 440 |
Release | : 2005-08-22 |
Genre | : Mathematics |
ISBN | : 9780521857000 |
Download Algebraic Statistics for Computational Biology Book in PDF, ePub and Kindle
This book, first published in 2005, offers an introduction to the application of algebraic statistics to computational biology.
Author | : Günter Harder |
Publisher | : Springer Science & Business Media |
Total Pages | : 376 |
Release | : 2011-04-21 |
Genre | : Mathematics |
ISBN | : 3834881597 |
Download Lectures on Algebraic Geometry II Book in PDF, ePub and Kindle
This second volume introduces the concept of shemes, reviews some commutative algebra and introduces projective schemes. The finiteness theorem for coherent sheaves is proved, here again the techniques of homological algebra and sheaf cohomology are needed. In the last two chapters, projective curves over an arbitrary ground field are discussed, the theory of Jacobians is developed, and the existence of the Picard scheme is proved. Finally, the author gives some outlook into further developments- for instance étale cohomology- and states some fundamental theorems.
Author | : Adriano M. Garsia |
Publisher | : Springer |
Total Pages | : 232 |
Release | : 2020-10-07 |
Genre | : Mathematics |
ISBN | : 9783030583729 |
Download Lectures in Algebraic Combinatorics Book in PDF, ePub and Kindle
Capturing Adriano Garsia's unique perspective on essential topics in algebraic combinatorics, this book consists of selected, classic notes on a number of topics based on lectures held at the University of California, San Diego over the past few decades. The topics presented share a common theme of describing interesting interplays between algebraic topics such as representation theory and elegant structures which are sometimes thought of as being outside the purview of classical combinatorics. The lectures reflect Garsia’s inimitable narrative style and his exceptional expository ability. The preface presents the historical viewpoint as well as Garsia's personal insights into the subject matter. The lectures then start with a clear treatment of Alfred Young's construction of the irreducible representations of the symmetric group, seminormal representations and Morphy elements. This is followed by an elegant application of SL(2) representations to algebraic combinatorics. The last two lectures are on heaps, continued fractions and orthogonal polynomials with applications, and finally there is an exposition on the theory of finite fields. The book is aimed at graduate students and researchers in the field.
Author | : Cristiano Bocci |
Publisher | : Springer Nature |
Total Pages | : 235 |
Release | : 2019-09-11 |
Genre | : Mathematics |
ISBN | : 3030246248 |
Download An Introduction to Algebraic Statistics with Tensors Book in PDF, ePub and Kindle
This book provides an introduction to various aspects of Algebraic Statistics with the principal aim of supporting Master’s and PhD students who wish to explore the algebraic point of view regarding recent developments in Statistics. The focus is on the background needed to explore the connections among discrete random variables. The main objects that encode these relations are multilinear matrices, i.e., tensors. The book aims to settle the basis of the correspondence between properties of tensors and their translation in Algebraic Geometry. It is divided into three parts, on Algebraic Statistics, Multilinear Algebra, and Algebraic Geometry. The primary purpose is to describe a bridge between the three theories, so that results and problems in one theory find a natural translation to the others. This task requires, from the statistical point of view, a rather unusual, but algebraically natural, presentation of random variables and their main classical features. The third part of the book can be considered as a short, almost self-contained, introduction to the basic concepts of algebraic varieties, which are part of the fundamental background for all who work in Algebraic Statistics.
Author | : Marlos A. G. Viana |
Publisher | : American Mathematical Soc. |
Total Pages | : 354 |
Release | : 2001 |
Genre | : Mathematics |
ISBN | : 0821826875 |
Download Algebraic Methods in Statistics and Probability Book in PDF, ePub and Kindle
The 23 papers report recent developments in using the technique to help clarify the relationship between phenomena and data in a number of natural and social sciences. Among the topics are a coordinate-free approach to multivariate exponential families, some rank-based hypothesis tests for covariance structure and conditional independence, deconvolution density estimation on compact Lie groups, random walks on regular languages and algebraic systems of generating functions, and the extendibility of statistical models. There is no index. c. Book News Inc.
Author | : Marcos Marino |
Publisher | : Springer |
Total Pages | : 219 |
Release | : 2008-08-15 |
Genre | : Mathematics |
ISBN | : 3540798145 |
Download Enumerative Invariants in Algebraic Geometry and String Theory Book in PDF, ePub and Kindle
Starting in the middle of the 80s, there has been a growing and fruitful interaction between algebraic geometry and certain areas of theoretical high-energy physics, especially the various versions of string theory. Physical heuristics have provided inspiration for new mathematical definitions (such as that of Gromov-Witten invariants) leading in turn to the solution of problems in enumerative geometry. Conversely, the availability of mathematically rigorous definitions and theorems has benefited the physics research by providing the required evidence in fields where experimental testing seems problematic. The aim of this volume, a result of the CIME Summer School held in Cetraro, Italy, in 2005, is to cover part of the most recent and interesting findings in this subject.
Author | : Giovanni Pistone |
Publisher | : CRC Press |
Total Pages | : 180 |
Release | : 2000-12-21 |
Genre | : Mathematics |
ISBN | : 1420035762 |
Download Algebraic Statistics Book in PDF, ePub and Kindle
Written by pioneers in this exciting new field, Algebraic Statistics introduces the application of polynomial algebra to experimental design, discrete probability, and statistics. It begins with an introduction to Grobner bases and a thorough description of their applications to experimental design. A special chapter covers the binary case