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Hammersley-Clifford theorem

Source: vignettes/hammersley-clifford.Rmd
hammersley-clifford.Rmd

This is based on Lusher, Koskinen, and Robins (2012).

Besag (1974)

This gives an alternative proof of the Hammersley-Clifford theorem and is used for spatial lattices.

Frank and Strauss (1986)

This paper shows that sufficient statistics for Markov graphs are counts of triangles and stars.

Robins and Pattison (2009)

This extends the types of graphs described including p*p^* models, and hence early ERGMs

References

Besag, Julian. 1974. “Spatial Interaction and the Statistical Analysis of Lattice Systems.” Journal of the Royal Statistical Society. Series B (Methodological) 36 (2): 192–236. https://www.jstor.org/stable/2984812.
Frank, Ove, and David Strauss. 1986. “Markov Graphs.” Journal of the American Statistical Association 81 (395): 832–42. https://doi.org/10.2307/2289017.
Lusher, Dean, Johan Koskinen, and Garry Robins. 2012. Exponential Random Graph Models for Social Networks: Theory, Methods, and Applications. Cambridge University Press.
Robins, Garry, and Philippa Pattison. 2009. “Interdependencies and Social Processes: Dependence Graphs and Generalized Dependence Structures.” In Models and Methods in Social Network Analysis, edited by Peter J. Carrington, John Scott, and Stanley Wasserman, Reprinted. Structural Analysis in the Social Sciences, 27 [i.e. 28]. Cambridge: Cambridge Univ. Press.