rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Markov Bases in Algebraic Statistics
  name:
    name part: Aoki, Satoshi.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Hara, Hisayuki.
    role:
      role term: author.
  name:
    name part: Takemura, Akimichi.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: xxu
    date issued: 2012
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XII, 300 p. online resource.
  abstract: 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. Satoshi Aoki obtained his doctoral degree from University of Tokyo in 2004 and is currently an associate professor in Graduate school of Science and Engineering, Kagoshima University. Hisayuki Hara obtained his doctoral degree from University of Tokyo in 1999 and is currently an associate professor in Faculty of Economics, Niigata University. Akimichi Takemura obtained his doctoral degree from Stanford University in 1982 and is currently a professor in Graduate School of Information Science and Technology, University of Tokyo.
  table of contents: 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.
  note: by Satoshi Aoki, Hisayuki Hara, Akimichi Takemura.
  subject:
    topic: Statistics
  subject:
    topic: Algebra
  subject:
    topic: Applied mathematics
  subject:
    topic: Engineering mathematics
  subject:
    topic: Statistics
  subject:
    topic: Statistics, general
  subject:
    topic: Statistical Theory and Methods
  subject:
    topic: General Algebraic Systems
  subject:
    topic: Applications of Mathematics
  classification: QA276-280
  classification: 519.5
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Springer Series in Statistics, 199
  identifier: 9781461437192
  identifier: http://dx.doi.org/10.1007/978-1-4614-3719-2
  record info:
    record creation date: 120723
    record change date: 20151125142151.0
    record identifier: 978-1-4614-3719-2