Markov bases in algebraic statistics. (English) Zbl 1304.62015
Springer Series in Statistics. New York, NY: Springer (ISBN 978-1-4614-3718-5/hbk; 978-1-4614-3719-2/ebook). xi, 298 p. (2012).
Publisher’s description: 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 P. Diaconis and B. Sturmfels [Ann. Stat. 26, No. 1, 363–397 (1998; Zbl 0952.62088)] 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.
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.
MSC:
62-02 | Research exposition (monographs, survey articles) pertaining to statistics |
13P10 | Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) |
13P25 | Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.) |
60J22 | Computational methods in Markov chains |
62F03 | Parametric hypothesis testing |
62H17 | Contingency tables |
62M99 | Inference from stochastic processes |
65C60 | Computational problems in statistics (MSC2010) |