Markov Bases in Algebraic Statistics

• Κύριοι συγγραφείς: Aoki, Satoshi (Συγγραφέας), Hara, Hisayuki (Συγγραφέας), Takemura, Akimichi (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: New York, NY : Springer New York : Imprint: Springer, 2012.
• Σειρά: Springer Series in Statistics, 199
• Θέματα: Statistics.; Algebra.; Applied mathematics.; Engineering mathematics.; Statistics, general.; Statistical Theory and Methods.; General Algebraic Systems.; Applications of Mathematics.

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 p...

Πίνακας περιεχομένων:

• Exact tests for contingency tables and discrete exponential families
• Markov chain Monte Carlo methods over discrete sample space
• Toric ideals and their Gröbner 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
• Gröbner basis techniques for design of experiments
• Running Markov chain without Markov bases
• References
• Index.