A bayesian approach to modeling stochastic blockstructures with covariates

Journal of Mathematical Sociology

Volumn 29, Issue 1, 2005, Pages 1-23

  Tallberg, Christian ^a  

^a STOCKHOLM UNIVERSITY   (Sweden)

Author keywords

Bayesian analysis; Blockmodels; Gibbs sampling; Multinomial probit; Random graphs

Indexed keywords

EID: 11844285672     PISSN: 0022250X     EISSN: None     Source Type: Journal    
DOI: 10.1080/00222500590889703     Document Type: Article

References (29)

1. Aitchison, J. & Bennett, J. A. (1970). Polychotomons quantal response by maximum indicant. Biometrica, 57, 263-202.
2. Albert, J. & Chib, S. (1993). Bayesian analysis of binary and polychotomous data. Journal, of the American Statistical Association, 88, 669-679.
3. Chib, S. (1995). Marginal likelihood from the Gibbs output, Journal of the American Statistical Association, 90, 1313-1321.
4. Chib, S. & Jeliazkov, I. (2001). Marginal likelihood from the Metropolis-Hastings output. Journal of the American Statistical Association, 96, 270-281.
5. 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.
6. Frank, O. (1988a). Triad count statistics. Discrete Mathematics, 72, 141-149.
7. Frank, O. (1988b). Random sampling and social networks: A survey of various approaches, Mathematiques. Informatique el Science Humaines, 86, 19-33.
8. Frank, O. & Harary, F. (1982). Cluster inference by using transitivity indices in empirical graphs Journal of the American Statistical Association, 77, 835-840.
9. Frank, O. & Strauss, D. (1986). Markov graphs. Journal of the American statistical Association, 81, 832-842.
10. 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 cal Association, 85, 972-985.
11. Gelfand, A. E. & Smith, A. F. M. (1990). Sampling-based approaches to calculating marginal densities. Journal, of the American Statislical Association, 85, 398-409.
12. Geweke, J. (1991). Efficient simulation from the multivariate normal and stiulent-t distrlbutions subject to linear constraints, Computing Science and Statistics: Proceedings of the Twenty-Third Symposium on the Interface. Alexandria, VA: American Statistical Association, 571-578.
13. Gilks, W. R. Richardson, S. & Spiegelhlter, D. J. (1990), 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.
14. Hoff, P. D., Raftery, A. E., and Handcock, M. S, (2002). Latent space approaches to social network analysis, & Jaurnal of the American Statistical Association, 97, 1090-1098.
15. Holland, P. Laskey, K. B. & Leinhardt, S. (1983), Stochastic blockmodels Home first stops, Social Networks, 5, 109-137.
16. Holland, P. & Leinhardt, S. (1981). An exponential family of probability distributions for directed graphs. Journal of the American Statistical. Association, 76, 33-65.
17. 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.
18. Koop, G & Poirier, D. (1993). Bayesian analysis of logit models using natural conjugate priors, Journal of Econometrics, 56, 323-340.
19. Koskinen, J. & Tallberg, C. (2004). A Bayesian approach to estimate the number of blocks in blockmodels. (Work in progress).
20. 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.
21. McCulloch, R. & Rossi, P. E. (1994), An exact likelihood analysis of the multinominal probit model, Journal of Econometrics, 04, 207-240.
22. Nowicki, K. & Snijders, T. A. B. (2001). Estimation and prediction for stochastic block-structures. Journal of the American Statistical Association, 96, 1077-1087.
23. 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.
24. Snijders, T. A. B. & Nowicki, K. (1997). Estimation and prediction for stochastic blockmodels for graphs with latent blockstrucutre. Journal of classification, 14, 75-100.
25. Wang, Y. J. & Wong, G. Y. (1987), Stochastic blockmodels for directed graphs. Journal of the American Statistical Association, 82, 8-19.
26. Wasserman. S & Anderson, C. (1987). Stochastic a posteriori block-models: Construction and assessment., Social Networks, 9, 1-30.
27. Wassermun, S. & Faust, K. (1994). Social Network Analysis: Methods and Applications, New York: Cambridge University Press.
28. 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.
29. Wong, G. Y. (1987). Bayesian models for directed graphs. Journal of the American Statistical. Association, 32, 140-148.