메뉴 건너뛰기




Volumn 17, Issue 4, 2007, Pages 1273-1297

Algebraic statistical models

Author keywords

Algebraic statistics; Computational algebraic geometry; Exponential family; Maximum likelihood estimation; Model invariants; Singularities

Indexed keywords


EID: 38549097237     PISSN: 10170405     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (36)

References (32)
  • 1
    • 0242607587 scopus 로고    scopus 로고
    • Phylogenetic invariants for the general Markov model of sequence mutation
    • Allman, E. S. and Rhodes, J. A. (2003). Phylogenetic invariants for the general Markov model of sequence mutation. Math. Biosci. 186, 113-144.
    • (2003) Math. Biosci , vol.186 , pp. 113-144
    • Allman, E.S.1    Rhodes, J.A.2
  • 2
    • 29244455841 scopus 로고    scopus 로고
    • Markov chain Monte Carlo exact tests for incomplete two-way contingency tables
    • Aoki, S. and Takemura, A. (2005). Markov chain Monte Carlo exact tests for incomplete two-way contingency tables. J. Stat. Comput. Simul. 75, 787-812.
    • (2005) J. Stat. Comput. Simul , vol.75 , pp. 787-812
    • Aoki, S.1    Takemura, A.2
  • 6
    • 0003369432 scopus 로고
    • Fundamentals of Statistical Exponential Families with Applications in Statistical Decision Theory
    • of, Institute of Mathematical Statistics, Hayward, CA
    • Brown, L. D. (1986). Fundamentals of Statistical Exponential Families with Applications in Statistical Decision Theory, vol. 9 of Institute of Mathematical Statistics Lecture Notes - Monograph Series. Institute of Mathematical Statistics, Hayward, CA.
    • (1986) Institute of Mathematical Statistics Lecture Notes - Monograph Series , vol.9
    • Brown, L.D.1
  • 8
    • 0000427391 scopus 로고
    • Gröbner bases of ideals of minors of a symmetric matrix
    • Conca, A. (1994). Gröbner bases of ideals of minors of a symmetric matrix. J. Algebra 166, 406-421.
    • (1994) J. Algebra , vol.166 , pp. 406-421
    • Conca, A.1
  • 10
    • 17044403041 scopus 로고    scopus 로고
    • Closures of exponential families
    • Csiszár, I. and Matúš, F. (2005). Closures of exponential families. Ann. Probab. 33, 582-600.
    • (2005) Ann. Probab , vol.33 , pp. 582-600
    • Csiszár, I.1    Matúš, F.2
  • 11
    • 0000508704 scopus 로고
    • Conditional independence for statistical operations
    • Dawid, A. R (1980). Conditional independence for statistical operations. Ann. Statist. 8, 598-617.
    • (1980) Ann. Statist , vol.8 , pp. 598-617
    • Dawid, A.R.1
  • 12
    • 0003212162 scopus 로고
    • Group Representations in Probability and Statistics
    • of, Institute of Mathematical Statistics, Hayward, CA
    • Diaconis, P. (1988). Group Representations in Probability and Statistics, vol. 11 of Institute of Mathematical Statistics Lecture Notes-Monograph Series. Institute of Mathematical Statistics, Hayward, CA.
    • (1988) Institute of Mathematical Statistics Lecture Notes-Monograph Series , vol.11
    • Diaconis, P.1
  • 13
    • 0032387555 scopus 로고    scopus 로고
    • Algebraic algorithms for sampling from conditional distributions
    • Diaconis, P. and Sturmfels, B. (1998). Algebraic algorithms for sampling from conditional distributions. Ann. Statist. 26, 363-397.
    • (1998) Ann. Statist , vol.26 , pp. 363-397
    • Diaconis, P.1    Sturmfels, B.2
  • 14
    • 4544259366 scopus 로고    scopus 로고
    • A divide-and-conquer algorithm for generating Markov bases of multi-way tables
    • Dobra, A. and Sullivant, S. (2004). A divide-and-conquer algorithm for generating Markov bases of multi-way tables. Comput. Statist. 19, 347-366.
    • (2004) Comput. Statist , vol.19 , pp. 347-366
    • Dobra, A.1    Sullivant, S.2
  • 15
    • 38549131930 scopus 로고    scopus 로고
    • Algebraic techniques for Gaussian models
    • Edited by M. Hušková and M. Janžura, Matfyzpress, Charles University Prague. arXiv:math.ST/0610679
    • Drton, M. (2006). Algebraic techniques for Gaussian models. In Prague Stochastics (Edited by M. Hušková and M. Janžura), 81-90. Matfyzpress, Charles University Prague. arXiv:math.ST/0610679
    • (2006) Prague Stochastics , pp. 81-90
    • Drton, M.1
  • 19
    • 0035612908 scopus 로고    scopus 로고
    • Stratified exponential families: Graphical models and model selection
    • Geiger, D., Heckerman, D., King, H. and Meek, C. (2001). Stratified exponential families: graphical models and model selection. Ann. Statist. 29, 505-529.
    • (2001) Ann. Statist , vol.29 , pp. 505-529
    • Geiger, D.1    Heckerman, D.2    King, H.3    Meek, C.4
  • 20
    • 33745671177 scopus 로고    scopus 로고
    • On the toric algebra of graphical models
    • Geiger, D., Meek, C. and Sturmfels, B. (2006). On the toric algebra of graphical models. Ann. Statist. 34, 1463-1492.
    • (2006) Ann. Statist , vol.34 , pp. 1463-1492
    • Geiger, D.1    Meek, C.2    Sturmfels, B.3
  • 21
    • 24344437315 scopus 로고    scopus 로고
    • Monomial ideals and the Scarf complex for coherent systems in reliability theory
    • Giglio, B. and Wynn, H. P. (2004). Monomial ideals and the Scarf complex for coherent systems in reliability theory. Ann. Statist. 32, 1289-1311.
    • (2004) Ann. Statist , vol.32 , pp. 1289-1311
    • Giglio, B.1    Wynn, H.P.2
  • 24
    • 0004047518 scopus 로고    scopus 로고
    • The Clarendon Press, Oxford University Press, New York
    • Lauritzen, S. L. (1996). Graphical Models. The Clarendon Press, Oxford University Press, New York.
    • (1996) Graphical Models
    • Lauritzen, S.L.1
  • 25
    • 0042788746 scopus 로고    scopus 로고
    • What is a statistical model?
    • McCullagh, P. (2002) What is a statistical model? Ann. Statist. 30, 1225-1310.
    • (2002) Ann. Statist , vol.30 , pp. 1225-1310
    • McCullagh, P.1
  • 26
    • 1542407746 scopus 로고    scopus 로고
    • Stochastic factorizations, sandwiched simplices and the topology of the space of explanations
    • Mond, D., Smith, J. and van Straten, D. (2003). Stochastic factorizations, sandwiched simplices and the topology of the space of explanations. R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci. 459, 2821-2845.
    • (2003) R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci , vol.459 , pp. 2821-2845
    • Mond, D.1    Smith, J.2    van Straten, D.3
  • 30
    • 15944419142 scopus 로고    scopus 로고
    • Toric ideals of phylogenetic invariants
    • Sturmfels, B. and Sullivant, S. (2005). Toric ideals of phylogenetic invariants. J. Comp. Biology 12, 204-228.
    • (2005) J. Comp. Biology , vol.12 , pp. 204-228
    • Sturmfels, B.1    Sullivant, S.2
  • 31
    • 33845708357 scopus 로고    scopus 로고
    • Distance-reducing Markov bases for sampling from a discrete sample space
    • Takemura, A. and Aoki, S. (2005). Distance-reducing Markov bases for sampling from a discrete sample space. Bernoulli 11, 793-813.
    • (2005) Bernoulli , vol.11 , pp. 793-813
    • Takemura, A.1    Aoki, S.2
  • 32
    • 70449475784 scopus 로고    scopus 로고
    • Algebraic Methods in Statistics and Probability
    • of, American Mathematical Society, Providence, RI
    • Viana, M. A. G. and Richards, D. S. P. (2001). Algebraic Methods in Statistics and Probability, Vol. 287 of Contemporary Mathematics. American Mathematical Society, Providence, RI.
    • (2001) Contemporary Mathematics , vol.287
    • Viana, M.A.G.1    Richards, D.S.P.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.