MARC Record from marc_columbia

LEADER: 08852cam a2200841 i 4500
001 13790440
005 20190313134457.0
008 180601s2018 riua b 001 0 eng
010 $a 2018025744
035 $a(OCoLC)on1044867449
040 $aDLC$beng$erda$cDLC$dOCLCF$dOCLCO$dYDX$dJHE$dYDX$dOCLCO$dNRC$dUKMGB$dHF9$dCOD$dCUY
015 $aGBB916449$2bnb
016 7 $a019219620$2Uk
020 $a9781470435172$qhardcover$qalkaline paper
020 $a1470435179$qhardcover$qalkaline paper
035 $a(OCoLC)1044867449
042 $apcc
050 00 $aQA276$b.S8945 2018
082 00 $a519.5$223
084 $a62-01$a14-01$a13P10$a13P15$a14M12$a14M25$a14P10$a14T05$a52B20$a60J10$a62F03$a62H17$a90C10$a92D15$2msc
049 $aZCUA
100 1 $aSullivant, Seth,$eauthor.
245 10 $aAlgebraic statistics /$cSeth Sullivant.
264 1 $aProvidence, Rhode Island :$bAmerican Mathematical Society,$c[2018]
300 $axiii, 490 pages :$billustrations ;$c26 cm.
336 $atext$btxt$2rdacontent
337 $aunmediated$bn$2rdamedia
338 $avolume$bnc$2rdacarrier
490 1 $aGraduate studies in mathematics ;$v194
504 $aIncludes bibliographical references and index.
505 0 $aCover; Title page; Preface; Chapter 1. Introduction; 1.1. Discrete Markov Chain; 1.2. Exercises; Chapter 2. Probability Primer; 2.1. Probability; 2.2. Random Variables and their Distributions; 2.3. Expectation, Variance, and Covariance; 2.4. Multivariate Normal Distribution; 2.5. Limit Theorems; 2.6. Exercises; Chapter 3. Algebra Primer; 3.1. Varieties; 3.2. Ideals; 3.3. Gröbner Bases; 3.4. First Applications of Gröbner Bases; 3.5. Computational Algebra Vignettes; 3.6. Projective Space and Projective Varieties; 3.7. Exercises; Chapter 4. Conditional Independence
505 8 $a4.1. Conditional Independence Models4.2. Primary Decomposition; 4.3. Primary Decomposition of CI Ideals; 4.4. Exercises; Chapter 5. Statistics Primer; 5.1. Statistical Models; 5.2. Types of Data; 5.3. Parameter Estimation; 5.4. Hypothesis Testing; 5.5. Bayesian Statistics; 5.6. Exercises; Chapter 6. Exponential Families; 6.1. Regular Exponential Families; 6.2. Discrete Regular Exponential Families; 6.3. Gaussian Regular Exponential Families; 6.4. Real Algebraic Geometry; 6.5. Algebraic Exponential Families; 6.6. Exercises; Chapter 7. Likelihood Inference
505 8 $a7.1. Algebraic Solution of the Score Equations7.2. Likelihood Geometry; 7.3. Concave Likelihood Functions; 7.4. Likelihood Ratio Tests; 7.5. Exercises; Chapter 8. The Cone of Sufficient Statistics; 8.1. Polyhedral Geometry; 8.2. Discrete Exponential Families; 8.3. Gaussian Exponential Families; 8.4. Exercises; Chapter 9. Fisher's Exact Test; 9.1. Conditional Inference; 9.2. Markov Bases; 9.3. Markov Bases for Hierarchical Models; 9.4. Graver Bases and Applications; 9.5. Lattice Walks and Primary Decompositions; 9.6. Other Sampling Strategies; 9.7. Exercises; Chapter 10. Bounds on Cell Entries
505 8 $a10.1. Motivating Applications10.2. Integer Programming and Gröbner Bases; 10.3. Quotient Rings and Gröbner Bases; 10.4. Linear Programming Relaxations; 10.5. Formulas for Bounds on Cell Entries; 10.6. Exercises; Chapter 11. Exponential Random Graph Models; 11.1. Basic Setup; 11.2. The Beta Model and Variants; 11.3. Models from Subgraphs Statistics; 11.4. Exercises; Chapter 12. Design of Experiments; 12.1. Designs; 12.2. Computations with the Ideal of Points; 12.3. The Gröbner Fan and Applications; 12.4. Two-level Designs and System Reliability; 12.5. Exercises; Chapter 13. Graphical Models
505 8 $a13.1. Conditional Independence Description of Graphical Models13.2. Parametrizations of Graphical Models; 13.3. Failure of the Hammersley-Clifford Theorem; 13.4. Examples of Graphical Models from Applications; 13.5. Exercises; Chapter 14. Hidden Variables; 14.1. Mixture Models; 14.2. Hidden Variable Graphical Models; 14.3. The EM Algorithm; 14.4. Exercises; Chapter 15. Phylogenetic Models; 15.1. Trees and Splits; 15.2. Types of Phylogenetic Models; 15.3. Group-based Phylogenetic Models; 15.4. The General Markov Model; 15.5. The Allman-Rhodes-Draisma-Kuttler Theorem; 15.6. Exercises
520 $aAlgebraic statistics uses tools from algebraic geometry, commutative algebra, combinatorics, and their computational sides to address problems in statistics and its applications. The starting point for this connection is the observation that many statistical models are semialgebraic sets. The algebra/statistics connection is now over twenty years old, and this book presents the first broad introductory treatment of the subject. Along with background material in probability, algebra, and statistics, this book covers a range of topics in algebraic statistics including algebraic exponential families, likelihood inference, Fisher's exact test, bounds on entries of contingency tables, design of experiments, identifiability of hidden variable models, phylogenetic models, and model selection. With numerous examples, references, and over 150 exercises, this book is suitable for both classroom use and independent study. -- Provided by publisher.
650 0 $aMathematical statistics$vTextbooks.
650 0 $aGeometry, Algebraic$vTextbooks.
650 7 $aStatistics -- Instructional exposition (textbooks, tutorial papers, etc.).$2msc
650 7 $aAlgebraic geometry -- Instructional exposition (textbooks, tutorial papers, etc.).$2msc
650 7 $aCommutative algebra -- Computational aspects and applications -- Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases).$2msc
650 7 $aCommutative algebra -- Computational aspects and applications -- Solving polynomial systems; resultants.$2msc
650 7 $aAlgebraic geometry -- Special varieties -- Determinantal varieties.$2msc
650 7 $aAlgebraic geometry -- Special varieties -- Toric varieties, Newton polyhedra.$2msc
650 7 $aAlgebraic geometry -- Real algebraic and real analytic geometry -- Semialgebraic sets and related spaces.$2msc
650 7 $aAlgebraic geometry -- Tropical geometry -- Tropical geometry.$2msc
650 7 $aConvex and discrete geometry -- Polytopes and polyhedra -- Lattice polytopes (including relations with commutative algebra and algebraic geometry).$2msc
650 7 $aProbability theory and stochastic processes -- Markov processes -- Markov chains (discrete-time Markov processes on discrete state spaces).$2msc
650 7 $aStatistics -- Parametric inference -- Hypothesis testing.$2msc
650 7 $aStatistics -- Multivariate analysis -- Contingency tables.$2msc
650 7 $aOperations research, mathematical programming -- Mathematical programming -- Integer programming.$2msc
650 7 $aBiology and other natural sciences -- Genetics and population dynamics -- Problems related to evolution.$2msc
650 7 $aGeometry, Algebraic.$2fast$0(OCoLC)fst00940902
650 7 $aMathematical statistics.$2fast$0(OCoLC)fst01012127
650 4 $aStatistics -- Instructional exposition (textbooks, tutorial papers, etc.).
650 4 $aAlgebraic geometry -- Instructional exposition (textbooks, tutorial papers, etc.).
650 4 $aCommutative algebra -- Computational aspects and applications -- Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases).
650 4 $aCommutative algebra -- Computational aspects and applications -- Solving polynomial systems; resultants.
650 4 $aAlgebraic geometry -- Special varieties -- Determinantal varieties.
650 4 $aAlgebraic geometry -- Special varieties -- Toric varieties, Newton polyhedra.
650 4 $aAlgebraic geometry -- Real algebraic and real analytic geometry -- Semialgebraic sets and related spaces.
650 4 $aAlgebraic geometry -- Tropical geometry -- Tropical geometry.
650 4 $aConvex and discrete geometry -- Polytopes and polyhedra -- Lattice polytopes (including relations with commutative algebra and algebraic geometry).
650 4 $aProbability theory and stochastic processes -- Markov processes -- Markov chains (discrete-time Markov processes on discrete state spaces).
650 4 $aStatistics -- Parametric inference -- Hypothesis testing.
650 4 $aStatistics -- Multivariate analysis -- Contingency tables.
650 4 $aOperations research, mathematical programming -- Mathematical programming -- Integer programming.
650 4 $aBiology and other natural sciences -- Genetics and population dynamics -- Problems related to evolution.
650 4 $aGeometry, Algebraic.$0(OCoLC)fst00940902
650 4 $aMathematical statistics.$0(OCoLC)fst01012127
655 7 $aTextbooks.$2fast$0(OCoLC)fst01423863
830 0 $aGraduate studies in mathematics ;$vv. 194.
852 00 $bmat$hQA276$i.S8945 2018