메뉴 건너뛰기




Volumn 34, Issue 2, 2006, Pages 939-972

Characterizing Markov equivalence classes for AMP chain graph models

Author keywords

Chain graph; Essential graph; Graphical model; Markov equivalence

Indexed keywords


EID: 33745294064     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/009053606000000173     Document Type: Article
Times cited : (16)

References (29)
  • 2
    • 0031477121 scopus 로고    scopus 로고
    • On the Markov equivalence of chain graphs, undirected graphs and acyclic digraphs
    • MR1436624
    • ANDERSSON, S. A., MADIGAN, D. and PERLMAN, M. D. (1997). On the Markov equivalence of chain graphs, undirected graphs and acyclic digraphs. Scand. J. Statist. 24 81-102. MR1436624
    • (1997) Scand. J. Statist. , vol.24 , pp. 81-102
    • Andersson, S.A.1    Madigan, D.2    Perlman, M.D.3
  • 3
    • 0031531764 scopus 로고    scopus 로고
    • A characterization of Markov equivalence classes for acyclic digraphs
    • MR1439312
    • ANDERSSON, S. A., MADIGAN, D. and PERLMAN, M. D. (1997). A characterization of Markov equivalence classes for acyclic digraphs. Ann. Statist. 25 505-541. MR1439312
    • (1997) Ann. Statist. , vol.25 , pp. 505-541
    • Andersson, S.A.1    Madigan, D.2    Perlman, M.D.3
  • 4
    • 0035285942 scopus 로고    scopus 로고
    • Alternative Markov properties for chain graphs
    • MR1844349
    • ANDERSSON, S. A., MADIGAN, D. and PERLMAN, M. D. (2001). Alternative Markov properties for chain graphs. Scand. J. Statist. 28 33-85. MR1844349
    • (2001) Scand. J. Statist. , vol.28 , pp. 33-85
    • Andersson, S.A.1    Madigan, D.2    Perlman, M.D.3
  • 5
    • 84896546661 scopus 로고    scopus 로고
    • Characterizing Markov equivalence classes for AMP chain graph models
    • Dept. Statistics, Univ. Washington
    • ANDERSSON, S. A. and PERLMAN, M. D. (2004). Characterizing Markov equivalence classes for AMP chain graph models. Technical Report 453, Dept. Statistics, Univ. Washington. Available at www.stat.washington.edu/www/research/ reports/2004/tr453.pdf.
    • (2004) Technical Report , vol.453
    • Andersson, S.A.1    Perlman, M.D.2
  • 7
    • 0001891186 scopus 로고
    • An introduction to chordal graphs and clique trees
    • (A. George, J. R. Gilbert and J. W. H. Liu, eds.) Springer, New York. MR1320296
    • BLAIR, J. R. S. and PEYTON, B. (1993). An introduction to chordal graphs and clique trees. In Graph Theory and Sparse Matrix Computation (A. George, J. R. Gilbert and J. W. H. Liu, eds.) 1-29. Springer, New York. MR1320296
    • (1993) Graph Theory and Sparse Matrix Computation , pp. 1-29
    • Blair, J.R.S.1    Peyton, B.2
  • 9
    • 0001842471 scopus 로고
    • Chain graphs for learning
    • (P. Besnard and S. Hanks, eds.) Morgan Kaufmann, San Francisco. MR1615011
    • BUNTINE, W. L. (1995). Chain graphs for learning. In Uncertainty in Artificial Intelligence: Proc. Eleventh Conference (P. Besnard and S. Hanks, eds.) 46-54. Morgan Kaufmann, San Francisco. MR1615011
    • (1995) Uncertainty in Artificial Intelligence: Proc. Eleventh Conference , pp. 46-54
    • Buntine, W.L.1
  • 10
    • 84858917594 scopus 로고    scopus 로고
    • Learning essential graph Markov models from data
    • (J. A. Gámez, S. Moral and A. Salmerón, eds.) Springer, Berlin. MR2090887
    • CASTELO, R. and PERLMAN, M. D. (2004). Learning essential graph Markov models from data. In Advances in Bayesian Networks (J. A. Gámez, S. Moral and A. Salmerón, eds.) 255-269. Springer, Berlin. MR2090887
    • (2004) Advances in Bayesian Networks , pp. 255-269
    • Castelo, R.1    Perlman, M.D.2
  • 12
    • 0007264891 scopus 로고    scopus 로고
    • Graphical Markov models: Statistical motivation
    • Paper presented Fields Institute for Research in Mathematical Sciences, Toronto, Canada
    • COX, D. R. (1999). Graphical Markov models: Statistical motivation. Paper presented at the Workshop on Conditional Independence Structures and Graphical Models, Fields Institute for Research in Mathematical Sciences, Toronto, Canada.
    • (1999) Workshop on Conditional Independence Structures and Graphical Models
    • Cox, D.R.1
  • 14
    • 33745306526 scopus 로고    scopus 로고
    • Maximum likelihood estimation in Gaussian chain graph models under the alternative Markov property
    • DRTON, M. and EICHLER, M. (2006). Maximum likelihood estimation in Gaussian chain graph models under the alternative Markov property. Scand. J. Statist. 33 247-258.
    • (2006) Scand. J. Statist. , vol.33 , pp. 247-258
    • Drton, M.1    Eichler, M.2
  • 15
    • 0001546180 scopus 로고
    • The chain graph Markov property
    • MR1096723
    • FRYDENBERG, M. (1990). The chain graph Markov property. Scand. J. Statist. 17 333-353. MR1096723
    • (1990) Scand. J. Statist. , vol.17 , pp. 333-353
    • Frydenberg, M.1
  • 16
    • 0036783875 scopus 로고    scopus 로고
    • The size distribution for Markov equivalence classes of acyclic digraph models
    • MR1935281
    • GILLISPIE, S. and PERLMAN, M. D. (2002). The size distribution for Markov equivalence classes of acyclic digraph models. Artificial Intelligence 141 137-155. MR1935281
    • (2002) Artificial Intelligence , vol.141 , pp. 137-155
    • Gillispie, S.1    Perlman, M.D.2
  • 17
    • 0000857850 scopus 로고
    • BIFROST-Block recursive models induced from relevant knowledge, observations and statistical techniques
    • HØJSGAARD, S. and THIESSON, B. (1995). BIFROST-Block recursive models induced from relevant knowledge, observations and statistical techniques. Comput. Statist. Data Anal. 19 155-175.
    • (1995) Comput. Statist. Data Anal. , vol.19 , pp. 155-175
    • Højsgaard, S.1    Thiesson, B.2
  • 19
    • 0002480085 scopus 로고
    • Graphical models for associations between variables, some of which are qualitative and some quantitative
    • MR0981437
    • LAURITZEN, S. L. and WERMUTH, N. (1989). Graphical models for associations between variables, some of which are qualitative and some quantitative. Ann. Statist. 17 31-57. MR0981437
    • (1989) Ann. Statist. , vol.17 , pp. 31-57
    • Lauritzen, S.L.1    Wermuth, N.2
  • 20
    • 0035528164 scopus 로고    scopus 로고
    • Separation and completeness properties for AMP chain graph Markov models
    • MR1891745
    • LEVITZ, M., PERLMAN, M. D. and MADIGAN, D. (2001). Separation and completeness properties for AMP chain graph Markov models. Ann. Statist. 29 1751-1784. MR1891745
    • (2001) Ann. Statist. , vol.29 , pp. 1751-1784
    • Levitz, M.1    Perlman, M.D.2    Madigan, D.3
  • 21
    • 0000220791 scopus 로고    scopus 로고
    • Bayesian model averaging and model selection for Markov equivalence classes of acyclic digraphs
    • MADIGAN, D., ANDERSSON, S. A., PERLMAN, M. D. and VOLINSKY, C. T. (1996). Bayesian model averaging and model selection for Markov equivalence classes of acyclic digraphs. Comm. Statist. - Theory Methods 25 2493-2519.
    • (1996) Comm. Statist. - Theory Methods , vol.25 , pp. 2493-2519
    • Madigan, D.1    Andersson, S.A.2    Perlman, M.D.3    Volinsky, C.T.4
  • 22
    • 19744369870 scopus 로고    scopus 로고
    • A unified approach to the characterization of equivalence classes of DAGs, chain graphs with no flags and chain graphs
    • MR2188675
    • ROVERATO, A. (2005). A unified approach to the characterization of equivalence classes of DAGs, chain graphs with no flags and chain graphs. Scand. J. Statist. 32 295-312. MR2188675
    • (2005) Scand. J. Statist. , vol.32 , pp. 295-312
    • Roverato, A.1
  • 23
    • 0002115567 scopus 로고    scopus 로고
    • On separation criterion and recovery algorithm for chain graphs
    • (F. Jensen and E. Horvitz, eds.) Morgan Kaufmann, San Francisco. MR1617229
    • STUDENÝ, M. (1996). On separation criterion and recovery algorithm for chain graphs. In Uncertainty in Artificial Intelligence: Proc. Twelfth Conference (F. Jensen and E. Horvitz, eds.) 509-516. Morgan Kaufmann, San Francisco. MR1617229
    • (1996) Uncertainty in Artificial Intelligence: Proc. Twelfth Conference , pp. 509-516
    • Studený, M.1
  • 24
    • 0031206655 scopus 로고    scopus 로고
    • A recovery algorithm for chain graphs
    • MR1462716
    • STUDENÝ, M. (1997). A recovery algorithm for chain graphs. Internat. J. Approx. Reason. 17 265-293. MR1462716
    • (1997) Internat. J. Approx. Reason. , vol.17 , pp. 265-293
    • Studený, M.1
  • 25
    • 0002871673 scopus 로고    scopus 로고
    • Bayesian networks from the point of view of chain graphs
    • (G. F. Cooper and S. Moral, eds.) Morgan Kaufmann, San Francisco
    • STUDENÝ, M. (1998). Bayesian networks from the point of view of chain graphs. In Uncertainty in Artificial Intelligence: Proc. Fourteenth Conference (G. F. Cooper and S. Moral, eds.) 496-503. Morgan Kaufmann, San Francisco.
    • (1998) Uncertainty in Artificial Intelligence: Proc. Fourteenth Conference , pp. 496-503
    • Studený, M.1
  • 26
    • 0032356059 scopus 로고    scopus 로고
    • On chain graph models for description of conditional independence structure
    • MR1647685
    • STUDENT, M. and BOUCKAERT, R. R. (1998). On chain graph models for description of conditional independence structure. Ann. Statist. 26 1434-1495. MR1647685
    • (1998) Ann. Statist. , vol.26 , pp. 1434-1495
    • Student, M.1    Bouckaert, R.R.2
  • 27
    • 0010402046 scopus 로고    scopus 로고
    • A graphical characterization of the largest chain graphs
    • MR1685080
    • VOLF, M. and STUDENÝ, M. (1999). A graphical characterization of the largest chain graphs. Internat. J. Approx. Reason. 20 209-236. MR1685080
    • (1999) Internat. J. Approx. Reason. , vol.20 , pp. 209-236
    • Volf, M.1    Studený, M.2
  • 28
    • 0002515017 scopus 로고
    • On substantive research hypotheses, conditional independence graphs and graphical chain models
    • MR1049302
    • WERMUTH, N. and LAURITZEN, S. L. (1990). On substantive research hypotheses, conditional independence graphs and graphical chain models (with discussion). J. Roy. Statist. Soc. Ser. B 52 21-72. MR1049302
    • (1990) J. Roy. Statist. Soc. Ser. B , vol.52 , pp. 21-72
    • Wermuth, N.1    Lauritzen, S.L.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.