메뉴 건너뛰기




Volumn 28, Issue 1, 2001, Pages 33-85

Alternative Markov properties for chain graphs

Author keywords

Block recursive normal linear system; Chain graph; Graphical markov model; Markov equivalence; Markov properties

Indexed keywords


EID: 0035285942     PISSN: 03036898     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9469.00224     Document Type: Article
Times cited : (130)

References (41)
  • 1
    • 0000784685 scopus 로고    scopus 로고
    • Normal linear regression models with recursive graphical markov structure
    • Andersson, S. A. & Perlman, M. D. (1998). Normal linear regression models with recursive graphical Markov structure. J. Multivariate Anal. 66, 133-187.
    • (1998) J. Multivariate Anal. , vol.66 , pp. 133-187
    • Andersson, S.A.1    Perlman, M.D.2
  • 3
    • 0031477121 scopus 로고    scopus 로고
    • On the markov equivalence of chain graphs, undirected graphs, and acyclic digraphs
    • Andersson, S. A., Madigan, D. & Perlman, M. D. (1997a). On the Markov equivalence of chain graphs, undirected graphs, and acyclic digraphs. Scand. J. Statist. 24, 81-102.
    • (1997) Scand. J. Statist. , vol.24 , pp. 81-102
    • Andersson, S.A.1    Madigan, D.2    Perlman, M.D.3
  • 4
    • 0031531764 scopus 로고    scopus 로고
    • A characterization of markov equivalence classes for acyclic digraphs
    • Andersson, S. A., Madigan, D. & Perlman, M. D. (1997b). A characterization of Markov equivalence classes for acyclic digraphs. Ann. Statist. 25, 505-541.
    • (1997) Ann. Statist. , vol.25 , pp. 505-541
    • Andersson, S.A.1    Madigan, D.2    Perlman, M.D.3
  • 7
    • 0002013121 scopus 로고
    • A transformational characterization of equivalent bayesian network structures
    • eds P. Besnard and S. Hanks, Morgan Kaufman, San Francisco
    • Chickering, D. M. (1995). A transformational characterization of equivalent Bayesian network structures. In Uncertainty in artificial intelligence: proceedings of the eleventh conference (eds P. Besnard and S. Hanks), 87-98. Morgan Kaufman, San Francisco.
    • (1995) Uncertainty in Artificial Intelligence: Proceedings of the Eleventh Conference , pp. 87-98
    • Chickering, D.M.1
  • 9
    • 84972506446 scopus 로고
    • Linear dependencies represented by chain graphs (with discussion)
    • Cox, D. R. & Wermuth, N. (1993). Linear dependencies represented by chain graphs (with discussion). Statist. Sci. 8, 204-218; 241-217.
    • (1993) Statist. Sci. , vol.8 , pp. 204-218
    • Cox, D.R.1    Wermuth, N.2
  • 11
    • 0000508704 scopus 로고
    • Conditional independence for statistical operations
    • Dawid, A. P. (1980). Conditional independence for statistical operations. Ann. Statist. 8, 598-617.
    • (1980) Ann. Statist. , vol.8 , pp. 598-617
    • Dawid, A.P.1
  • 12
    • 21344482755 scopus 로고
    • Hyper Markov laws in the statistical analysis of decomposable graphical models
    • Dawid, A. P. & Lauritzen, S. L. (1993). Hyper Markov laws in the statistical analysis of decomposable graphical models. Ann. Statist. 21, 1272-1317.
    • (1993) Ann. Statist. , vol.21 , pp. 1272-1317
    • Dawid, A.P.1    Lauritzen, S.L.2
  • 13
    • 0001038826 scopus 로고
    • Covariance selection
    • Dempster, A. P. (1972). Covariance selection. Biometrics 28, 157-175.
    • (1972) Biometrics , vol.28 , pp. 157-175
    • Dempster, A.P.1
  • 15
    • 0001546180 scopus 로고
    • The chain graph Markov property
    • Frydenberg, M. (1990). The chain graph Markov property. Scand. J. Statist. 17, 333-353.
    • (1990) Scand. J. Statist. , vol.17 , pp. 333-353
    • Frydenberg, M.1
  • 16
    • 0002838461 scopus 로고
    • On the logic of influence diagrams
    • eds R. Shachter, T. Levitt, L. Kanal and J. Lemmer, North-Holland, Amsterdam
    • Geiger, D. & Pearl, J. (1988). On the logic of influence diagrams. In Proceedings of the 4th workshop on uncertainty in artificial intelligence (eds R. Shachter, T. Levitt, L. Kanal and J. Lemmer), 136-147. North-Holland, Amsterdam.
    • (1988) Proceedings of the 4th Workshop on Uncertainty in Artificial Intelligence , pp. 136-147
    • Geiger, D.1    Pearl, J.2
  • 17
    • 0000857850 scopus 로고
    • BIFROST - Block recursive models induced from relevant knowledge, observations, and statistical techniques
    • Højsgaard, S. & 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
  • 18
    • 0030555537 scopus 로고    scopus 로고
    • On a dualization of graphical gaussian models
    • Kauermann, G. (1996). On a dualization of graphical Gaussian models. Scand. J. Statist. 23, 105-116.
    • (1996) Scand. J. Statist. , vol.23 , pp. 105-116
    • Kauermann, G.1
  • 19
    • 0030374547 scopus 로고    scopus 로고
    • Markov properties of non-recursive causal models
    • Koster, J. T. A. (1996). Markov properties of non-recursive causal models. Ann. Statist. 24, 2148-2177.
    • (1996) Ann. Statist. , vol.24 , pp. 2148-2177
    • Koster, J.T.A.1
  • 20
  • 21
    • 0001006209 scopus 로고
    • Local computations with probabilities on graphical structures and their application to expert systems (with discussion)
    • Lauritzen, S. L. & Spiegelhalter, D. J. (1988). Local computations with probabilities on graphical structures and their application to expert systems (with discussion). J. Roy. Statist. Soc. Ser. B 50, 157-224.
    • (1988) J. Roy. Statist. Soc. Ser. B , vol.50 , pp. 157-224
    • Lauritzen, S.L.1    Spiegelhalter, D.J.2
  • 22
    • 0002480085 scopus 로고
    • Graphical models for association between variables, some of which are qualitative and some quantitative
    • Lauritzen, S. L. & Wermuth, N. (1989). Graphical models for association between variables, some of which are qualitative and some quantitative. Ann. Statist. 17, 31-57.
    • (1989) Ann. Statist. , vol.17 , pp. 31-57
    • Lauritzen, S.L.1    Wermuth, N.2
  • 24
  • 26
    • 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. & Volinsky, C. M. (1996). Bayesian model averaging and model selection for Markov equivalence classes of acyclic digraphs. Commun. Statist. Theory Methods 25, 2493-2519.
    • (1996) Commun. Statist. Theory Methods , vol.25 , pp. 2493-2519
    • Madigan, D.1    Andersson, S.A.2    Perlman, M.D.3    Volinsky, C.M.4
  • 27
    • 0007225314 scopus 로고
    • On equivalence of Markov properties over undirected graphs
    • Matús, F. (1992). On equivalence of Markov properties over undirected graphs. J. Appl. Probab. 29, 745-749.
    • (1992) J. Appl. Probab. , vol.29 , pp. 745-749
    • Matús, F.1
  • 30
  • 32
    • 0003263637 scopus 로고
    • Directed cyclic graphical representation of feedback models
    • eds P. Besnard and S. Hanks, Morgan Kaufmann, San Francisco
    • Spirtes, P. (1995). Directed cyclic graphical representation of feedback models. In Uncertainty in artificial intelligence: proceedings of the eleventh conference (eds P. Besnard and S. Hanks), 491-498. Morgan Kaufmann, San Francisco.
    • (1995) Uncertainty in Artificial Intelligence: Proceedings of the Eleventh Conference , pp. 491-498
    • Spirtes, P.1
  • 34
    • 0002115567 scopus 로고    scopus 로고
    • On separation criterion and recovery algorithm for chain graphs
    • eds F. Jensen and E. Horvitz, Morgan Kaufmann, San Francisco
    • Studený, M. (1996). On separation criterion and recovery algorithm for chain graphs. In Uncertainty in artificial intelligence: proceedings of the twelfth conference (eds F. Jensen and E. Horvitz), 509-516. Morgan Kaufmann, San Francisco.
    • (1996) Uncertainty in Artificial Intelligence: Proceedings of the Twelfth Conference , pp. 509-516
    • Studený, M.1
  • 35
  • 36
    • 0032356059 scopus 로고    scopus 로고
    • On chain graph models for description of conditional independence structure
    • Studený, M. & Bouckaert, R. R. (1998). On chain graph models for description of conditional independence structure. Ann. Statist. 26, 1434-1495.
    • (1998) Ann. Statist. , vol.26 , pp. 1434-1495
    • Studený, M.1    Bouckaert, R.R.2
  • 37
    • 0001775899 scopus 로고
    • An algorithm for deciding if a set of observed independencies has a causal explanation
    • eds D. Dubois, M. Wellman, B. D'Ambrosio, P. Smets, Morgan Kaufman, San Francisco
    • Verma, T. & Pearl, J. (1992). An algorithm for deciding if a set of observed independencies has a causal explanation. In Uncertainty in artificial intelligence: proceedings of the eighth conference (eds D. Dubois, M. Wellman, B. D'Ambrosio, P. Smets), 323-330. Morgan Kaufman, San Francisco.
    • (1992) Uncertainty in Artificial Intelligence: Proceedings of the Eighth Conference , pp. 323-330
    • Verma, T.1    Pearl, J.2
  • 38
    • 0000243504 scopus 로고
    • Graphical and recursive models for contingency tables
    • Wermuth, N. & Lauritzen, S. L. (1983). Graphical and recursive models for contingency tables. Biometrika 70, 537-552
    • (1983) Biometrika , vol.70 , pp. 537-552
    • Wermuth, N.1    Lauritzen, S.L.2
  • 39
    • 0002515017 scopus 로고
    • On substantive research hypotheses, conditional independence graphs, and graphical chain models (with discussion)
    • Wermuth, N. & 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.
    • (1990) J. Roy. Statist. Soc. Ser. B , vol.52 , pp. 21-72
    • Wermuth, N.1    Lauritzen, S.L.2
  • 41
    • 84946357749 scopus 로고
    • An efficient method of estimating seemingly unrelated regression equations and tests for aggregation bias
    • Zellner, A. (1962). An efficient method of estimating seemingly unrelated regression equations and tests for aggregation bias. J. Amer. Statist. Assoc. 57, 348-368.
    • (1962) J. Amer. Statist. Assoc. , vol.57 , pp. 348-368
    • Zellner, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.