Computational Statistical Methods for Social Network Models David R. Hunter, Pavel N. Krivitsky, and Michael Schweinberger ∗ September 11, 2012 Abstract This article reviews the broad range of recent statistical work in social network models, with particular emphasis on computational aspects of these methods. Keywords: degeneracy, ERGM, latent variables, MCMC MLE, variational methods 1 Introduction A typical statistical data frame includes sampling units, which may be considered individuals, and analysis often focuses on some property of these units. Loosely speaking, social networks arise whenever the “property” of interest involves interactions between multiple sampling units, rather than the units themselves. We do not limit ourselves to the case in which the sampling units are actually human beings, though this is by far the most common application that has appeared in the literature on social network models. There is a long history of work that may be characterized as related to social networks—as Carrington and Scott (2011) point out, it is difficult to pinpoint the genesis of this field but its roots may be traced at least as far back as the 1930s—though we do not focus on this development here, both because there already exist numerous treatises on networks in general and social networks in particular, and because for the audience of JCGS, we wish to focus on computational questions. However, we can at least give a partial list of survey-type references for readers interested in delving into the subject of social networks more deeply: Though almost two decades old, the * All three authors contributed equally to this article. 1