Markov Bases in Algebraic Statistics

Authors: Satoshi Aoki, Hisayuki Hara, Akimichi Takemura



Crucial guide for statisticians no matter previous exposure to algebra and algebraic statistics

Clear organization guides the reader through the 16 chapters with figures and tables

Shows topic in its broader context, beginning with introductory material

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.



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