Algebraic Methods In Statistics And Probability Ii
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Algebraic Methods in Statistics and Probability II
Author: Marlos A. G. Viana
language: en
Publisher: American Mathematical Soc.
Release Date: 2010
A decade after the publication of Contemporary Mathematics Vol. 287, the present volume demonstrates the consolidation of important areas, such as algebraic statistics, computational commutative algebra, and deeper aspects of graphical models. --
Algebraic Methods in Statistics and Probability
Author: Marlos A. G. Viana
language: en
Publisher: American Mathematical Soc.
Release Date: 2001
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.
Markov Bases in Algebraic Statistics
Author: Satoshi Aoki
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-07-25
Algebraic statistics is a rapidly developing field, where ideas from statistics and algebra meet and stimulate new research directions. One of the origins of algebraic statistics is the work by Diaconis and Sturmfels in 1998 on the use of Gröbner bases for constructing a connected Markov chain for performing conditional tests of a discrete exponential family. In this book we take up this topic and present a detailed summary of developments following the seminal work of Diaconis and Sturmfels. This book is intended for statisticians with minimal backgrounds in algebra. As we ourselves learned algebraic notions through working on statistical problems and collaborating with notable algebraists, we hope that this book with many practical statistical problems is useful for statisticians to start working on the field.