A BAYESIAN APPROACH TO MODELING STOCHASTIC BLOCKSTRUCTURES WITH COVARIATES

REFERENCES

• Aitchison , J. & Bennett , J. A. ( 1970 ). Polychotomous quantal response by maximum indicant . Biometrica , 57 , 253 – 262 .
   Web of Science ®Google Scholar
• Albert , J. & Chib , S. ( 1993 ). Bayesian analysis of binary and polychotomous data . Journal of the American Statistical Association , 88 , 669 – 679 .
   Web of Science ®Google Scholar
• Chib , S. (1995). Marginal likelihood from the Gibbs output, Journal of the American Statistical Association , 90, 1313–1321.
   Web of Science ®Google Scholar
• Chib , S. & Jeliazkov , I. ( 2001 ). Marginal likelihood from the Metropolis-Hastings output . Journal of the American Statistical Association , 96 , 270 – 281 . [CROSSREF]
   Web of Science ®Google Scholar
• Fienberg , S. E. & Wasserman , S. ( 1981 ). Categorical data analysis of aingle sociometric relations . In S. Leinhardt (ed.), Sociological Methodology-1981 , San Fransisco : Jossey-Bass , pp. 156 – 192 .
   Google Scholar
• Frank , O. ( 1988a ). Triad count statistics . Discrete Mathematics , 72 , 141 – 149 . [CROSSREF]
   Google Scholar
• Frank , O. ( 1988b ). Random sampling and social networks: A survey of various approaches . Mathematiques. Informatique et Sciences Humaines , 26 , 19 – 33 .
   Google Scholar
• Frank , O. & Harary , F. ( 1982 ). Cluster inference by using transitivity indices in empirical graphs Journal of the American Statistical Association , 77 , 835 – 840 .
   Google Scholar
• Frank , O. Strauss , D. ( 1986 ). Markov graphs . Journal of the American Statistical Association , 81 , 832 – 842 . [CSA]
   Web of Science ®Google Scholar
• Gelfand , A. E. Hills , S. E. Racine-Poon , A. and Smith , A. F. M. ( 1990 ). Illustration of Bayesian inference in normal data models using Gibbs sampling . Journal of the American Statistical Association , 85 , 972 – 985 .
   Web of Science ®Google Scholar
• Gelfand , A. E. & Smith , A. F. M. ( 1990 ). Sampling-based approaches to calculating marginal densities . Journal of the American Statistical Association , 85 , 398 – 409 .
   Web of Science ®Google Scholar
• Geweke , J. ( 1991 ) . Efficient simulation from the multivariate normal and student-t distributions subject to linear constraints , Computing Science and Statistics: Proceedings of the Twenty-Third Symposium on the Interface . Alexandria , VA : American Statistical Association , 571 – 578 .
   Google Scholar
• Gilks , W. R. Richardson , S. and Spiegelhalter , D. J. ( 1996 ). Introducing markov chain monte carlo . In W. R. Gilks , S. Richardson and D. J. Spiegelhalter (eds.), Markov Chain Monte Carlo in Practice (pp. 1 – 19 ). London : Chapman and Hall .
   Google Scholar
• Hoff , P. D. , Raftery , A. E. & Handcock , M. S. ( 2002 ). Latent space approaches to social network analysis , & Journal of the American Statistical Association , 97 , 1090 – 1098 . [CROSSREF]
   Web of Science ®Google Scholar
• Holland , P. Laskey , K. B. & Leinhardt , S. ( 1983 ). Stochastic blockmodels: Some first steps . Social Networks , 5 , 109 – 137 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Holland , P. & Leinhardt , S. ( 1981 ). An exponential family of probability distributions for directed graphs . Journal of the American Statistical Association , 76 , 33 – 65 .
   Web of Science ®Google Scholar
• Janson , S. & Nowicki , K. ( 1991 ). The asymptotic distributions of generalized U-statistics with applications to random graphs . Probability Theory and Related Fields , 90 , 341 – 375 .
   Google Scholar
• Koop , G & Poirier , D. ( 1993 ). Bayesian analysis of logit models using natural conjugate priors , Journal of Econometrics , 56 , 323 – 340 . [CROSSREF]
   Web of Science ®Google Scholar
• Koskinen , J. & Tallberg , C. ( 2004 ) . A Bayesian approach to estimate the number of blocks in blockmodels . (Work in progress) .
   Google Scholar
• McCulloch , R. Polson , N. G. & Rossi , P. E. ( 200 ). A Bayesian analysis of the multinomial probit model with fully identified parameters . Journal of Econometrics , 99 , 173 – 193 . [CROSSREF]
   Google Scholar
• McCulloch , R. & Rossi P. E. ( 1994 ). An exact likelihood analysis of the multinominal probit model . Journal of Econometrics , 64 , 207 – 240 . [CROSSREF]
   Web of Science ®Google Scholar
• Nowicki , K. & Snijders , T. A. B. ( 2001 ). Estimation and prediction for stochastic blockstructures . Journal of the American Statistical Association , 96 , 1077 – 1087 . [CROSSREF]
   Web of Science ®Google Scholar
• Richardson , S. & Green , P. J. ( 1997 ). On Bayesian analysis of mixtures with an unknown number of components . Journal of the Royal Statistical Society , 59 , 731 – 792 . [CROSSREF]
   Google Scholar
• Snijders , T. A. B. & Nowicki , K. ( 1997 ). Estimation and prediction for stochastic blockmodels for graphs with latent blockstrucutre . Journal of classification , 14 , 75 – 100 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Wang , Y. J. & Wong , G. Y. ( 1987 ). Stochastic blockmodels for directed graphs . Journal of the American Statistical Association , 82 , 8 – 19 .
   Web of Science ®Google Scholar
• Wasserman , S. & Anderson , C. (1987). Stochastic a posteriori block-models: Construction and assessment. Social Networks , 9, 1–36. [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Wasserman , S. & Faust , K. ( 1994 ) . Social Network Analysis: Methods and Applications , New York : Cambridge University Press .
   Google Scholar
• White , H. C. Boorman , S. & Breiger , R. L. ( 1976 ). Social structure from multiple networks. I. Blockmodels of roles and positions . American Journal of Sociology , 81 , 730 – 779 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Wong , G. Y. ( 1987 ). Bayesian models for directed graphs . Journal of the American Statistical Association , 82 , 140 – 148 .
   Web of Science ®Google Scholar