统计Markov Graphs - 人大经济论坛

人大经济论坛 › 经典文献» 浏览文献

Markov Graphs

文献名称	Markov Graphs
文献作者	Ove Frank; David Strauss
作者所在单位	Statistics Department, University of Stock-holm;Statistics Department, University of California
文献分类	已发表文献
学科一级分类	统计
学科二级分类	统计学
文献摘要	Log-linear statistical models are used to characterize random graphs with general dependence structure and with Markov dependence. Sufficient statistics for Markov graphs are shown to be given by counts of various triangles and stars. In particular, we show under which assumptions the triad counts are sufficient statistics. We discuss inference methodology for some simple Markov graphs.
参考文献	Besag, J. E. (1S Lattice System day, Ser. B, Fienberg, S., Meyer, M., and Wasserman, S. (1985), "Statistical Analysis of Multiple Sociometric Relations," Journal of the American Statistical Association, 80, 51-67. Frank, O. (1978), "Sampling and Estimation in Large Social Networks," Social Networks, 1, 91-101. (1979), "Estimating a Graph From Triad Counts," Journal of Statistical Computation and Simulation, 9, 31-46. Frank, 0., and Harary, F. (1982), "Cluster Inference by Using Transi- tivity Indices in Empirical Graphs," Journal of the American Statistical Association, 77, 835-840. Freeman, L. C., Romney, A. K., and White, D. R. (in press), "Research Methods in Network Analysis," Social Networks. Hammersley, J. M., and Handscomb, D. C. (1964), Monte Carlo Meth- ods, London: Methuen. Holland, P. W., and Leinhardt, S. (1981), "An Exponential Family of Probability Densities for Directed Graphs," Journal of the American Statistical Association, 76, 33-51. Karotiski, M. (1982), "A Review of Random Graphs," Journal of Graph Theory, 6, 349-389. Ogata, Y., and Tanemura, M. (1984). "Likelihood Analysis of Spatial Point Patterns," Journal of the Royal Statistical Society, Ser. B, 46, 496-518. Pickard, D. K. (1977), "Asymptotic Inference for an Ising Lattice II," Advances in Applied Probability, 9, 476-501. Rapoport, A. (1949), "Outline of a Probabilistic Approach to Animal Sociology 1I," Bulletin of Mathematical Biophysics, 2, 273-291. (1950), "Outline of a Probabilistic Approach to Animal Sociology III," Bulletin of Mathematical Biophysics, 12, 7-17. (1957), "Contribution to Theory of Random and Biased Nets," Bulletin of Mathematical Biophysics, 19, 257-277. (1979), "A Probabilistic Approach to Networks," Social Net- works, 2, 1-18. Ripley, B. (1981), Spatial Statistics, New York: John Wiley. Ruelle, D. (1969), Statistical Mechanics: Rigorous Results, New York: Benjamin. Speed, T. P. (1978), "Relations Between Models for Spatial Data, Con- tingency Tables and Markov Fields on Graphs," Supplement Advances in Applied Probability, 10, 111-122. Strauss, D. J. (1975), "A Model for Clustering," Biometrika, 62, 467- 475. (1977), "Clustering on Colored Lattices," Journal of Applied Probability, 14, 135-143. (in press), "On a General Class of Models for Interaction," SIAM Review Journal. Strauss, D. J., and Freeman, L. C. (in press), "Stochastic Modelling and the Analysis of Structural Data," Social Networks. Wasserman, S. (1980), "Analyzing Social Networks as Stochastic Pro- cesses," Journal of the American Statistical Association, 75, 280-294.
关键字	Log-linear network model; Markov field;Graph inference.
发表所在刊物（或来源）	Journal of the American Statistical Association, Vol. 81, No. 395 (Sep., 1986), 832-842.
发表时间	Sep., 1986
适用研究领域
评论
上传时间	2011-1-20 15:39
下载文献	strauss.pdf[1.5 MB] 注：下载文献会消耗您一个“当日剩余下载次数”
会员评论
发表评论