Markov bases in algebraic statistics
著者
書誌事項
Markov bases in algebraic statistics
（Springer series in statistics）
Springer, c2012
- : hbk
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注記
Includes bibliographical references (p. 287-293) and index
内容説明・目次
内容説明
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 Groebner 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.
目次
Exact tests for contingency tables and discrete exponential families.- Markov chain Monte Carlo methods over discrete sample space.- Toric ideals and their Groebner bases.- Definition of Markov bases and other bases.- Structure of minimal Markov bases.- Method of distance reduction.- Symmetry of Markov bases.- Decomposable models of contingency tables.- Markov basis for no-three-factor interaction models and some other hierarchical models.- Two-way tables with structural zeros and fixed subtable sums.- Regular factorial designs with discrete response variables.- Group-wise selection models.- The set of moves connecting specific fibers.- Disclosure limitation problem and Markov basis.- Groebner basis techniques for design of experiments.- Running Markov chain without Markov bases.- References.- Index.
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