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@Article{KrHu23e,
  author  = {Pavel N. Krivitsky and David R. Hunter and Martina Morris and Chad Klumb},
  title   = {{ergm} 4: New Features for Analyzing Exponential-Family Random Graph Models},
  journal = {Journal of Statistical Software},
  year    = {2023},
  volume  = {105},
  number  = {6},
  pages   = {1--44},
  doi     = {10.18637/jss.v105.i06},
}

@Article{HuHa08e,
  author  = {Hunter, David R. and Handcock, Mark S. and Butts, Carter T. and Goodreau, Steven M. and Morris, Martina},
  title   = {{ergm}: A Package to Fit, Simulate and Diagnose Exponential-Family Models for Networks},
  journal = {Journal of Statistical Software},
  year    = {2008},
  volume  = {24},
  number  = {3},
  pages   = {1--29},
  month   = may,
  doi     = {10.18637/jss.v024.i03},
}

@Article{DuGi09f,
  author  = {van Duijn, Marijtje A. J. and Gile, Krista J. and Handcock, Mark S.},
  title   = {A Framework for the Comparison of Maximum Pseudo-likelihood and Maximum Likelihood Estimation of Exponential Family Random Graph Models},
  journal = {Social Networks},
  year    = {2009},
  volume  = {31},
  number  = {1},
  pages   = {52--62},
  doi     = {10.1016/j.socnet.2008.10.003},
}

@InProceedings{ScDe17e,
  author       = {Schmid, Christian S and Desmarais, Bruce A},
  title        = {Exponential random graph models with big networks: Maximum pseudolikelihood estimation and the parametric bootstrap},
  booktitle    = {2017 IEEE international conference on big data (Big Data)},
  year         = {2017},
  pages        = {116--121},
  organization = {IEEE},
}

@Article{ScHu23c,
  author = {Christian S. Schmid and David R. Hunter},
  title = {Computing Pseudolikelihood Estimators for Exponential-Family Random Graph Models},
  journal = {Journal of Data Science},
  volume = {21},
  number = {2},
  year = {2023},
  pages = {295--309},
  doi = {10.6339/23-JDS1094},
}

@Article{HuHu12i,
  author   = {Hummel, Ruth M. and Hunter, David R. and Handcock, Mark S.},
  title    = {Improving Simulation-based Algorithms for Fitting {ERGMs}},
  journal  = {Journal of Computational and Graphical Statistics},
  year     = {2012},
  volume   = {21},
  number   = {4},
  pages    = {920--939},
  abstract = { Markov chain Monte Carlo methods can be used to approximate the intractable normalizing constants that arise in likelihood calculations for many exponential-family random graph models for networks. However, in practice, the resulting approximations degrade as parameter values move away from the value used to define the Markov chain, even in cases where the chain produces perfectly efficient samples. We introduce a new approximation method along with a novel method of moving toward a maximum likelihood estimator (MLE) from an arbitrary starting parameter value in a series of steps based on alternating between the canonical exponential-family parameterization and the mean-value parameterization. This technique enables us to find an approximate MLE in many cases where this was previously not possible. We illustrate these methods on a model for a transcriptional regulation network for E. coli, an example where previous attempts to approximate an MLE had failed, and a model for a well-known social network dataset involving friendships among workers in a tailor shop. These methods are implemented in the publicly available ergm package for R, and computer code to duplicate the results of this article is included in the online supplementary materials. },
  doi      = {10.1080/10618600.2012.679224},
}

@Article{HaGi10m,
  author   = {Handcock, Mark S. and Gile, Krista J.},
  title    = {Modeling Social Networks from Sampled Data},
  journal  = {Annals of Applied Statistics},
  year     = {2010},
  volume   = {4},
  number   = {1},
  pages    = {5--25},
  issn     = {1932-6157},
  abstract = {Network models are widely used to represent relational information among interacting units and the structural implications of these relations. Recently, social network studies have focused a great deal of attention on random graph models of networks whose nodes represent individual social actors and whose edges represent a specified relationship between the actors. Most inference for social network models assumes that the presence or absence of all possible links is observed, that the information is completely reliable, and that there are no measurement (e.g., recording) errors. This is clearly not true in practice, as much network data is collected though sample surveys. In addition even if a census of a population is attempted, individuals and links between individuals are missed (i.e., do not appear in the recorded data). In this paper we develop the conceptual and computational theory for inference based on sampled network information. We first review forms of network sampling designs used in practice. We consider inference from the likelihood framework, and develop a typology of network data that reflects their treatment within this frame. We then develop inference for social network models based on information from adaptive network designs. We motivate and illustrate these ideas by analyzing the effect of link-tracing sampling designs on a collaboration network.},
  doi      = {10.1214/08-AOAS221},
}

@Article{HuHa06i,
  author    = {Hunter, David R. and Handcock, Mark S.},
  title     = {Inference in Curved Exponential Family Models for Networks},
  journal   = {Journal of Computational and Graphical Statistics},
  year      = {2006},
  volume    = {15},
  number    = {3},
  pages     = {565--583},
  issn      = {1061-8600},
  doi       = {10.1198/106186006X133069},
  publisher = {American Statistical Association},
}

@Article{Sn02m,
  author  = {Snijders, Tom A. B.},
  title   = {{Markov chain Monte Carlo} Estimation of Exponential Random Graph Models},
  journal = {Journal of Social Structure},
  year    = {2002},
  volume  = {3},
  number  = {2},
}

@Article{StIk90p,
  author  = {Strauss, David and Ikeda, Michael},
  title   = {Pseudolikelihood Estimation for Social Networks},
  journal = {Journal of the American Statistical Association},
  year    = {1990},
  volume  = {85},
  number  = {409},
  pages   = {204--212},
  issn    = {0162-1459},
}

@Article{RoMo51s,
  author    = {Robbins, Herbert and Monro, Sutton},
  title     = {A Stochastic Approximation Method},
  journal   = {The Annals of Mathematical Statistics},
  year      = {1951},
  volume    = {22},
  number    = {3},
  pages     = {400--407},
  month     = sep,
  issn      = {00034851},
  abstract  = {Let M(x) denote the expected value at level x of the response to a certain experiment. M(x) is assumed to be a monotone function of x but is unknown to the experimenter, and it is desired to find the solution x = θ of the equation M(x) = α, where α is a given constant. We give a method for making successive experiments at levels x1,x2,⋯ in such a way that xn will tend to θ in probability.},
  copyright = {Copyright © 1951 Institute of Mathematical Statistics},
  publisher = {Institute of Mathematical Statistics},
}

@Article{Be74s,
  author        = {Besag, Julian},
  title         = {Spatial Interaction and the Statistical Analysis of Lattice Systems (with Discussion)},
  journal       = {Journal of the Royal Statistical Society, Series B},
  year          = {1974},
  volume        = {36},
  pages         = {192--236},
  issn          = {0035-9246},
  date-modified = {2007-03-13 22:41:28 -0700},
}

@Article{FrSt86m,
  author  = {Frank, Ove and Strauss, David},
  title   = {{Markov} Graphs},
  journal = {Journal of the American Statistical Association},
  year    = {1986},
  volume  = {81},
  number  = {395},
  pages   = {832--842},
  issn    = {0162-1459},
  doi     = {10.1080/01621459.1986.10478342},
}

@Article{Kr17u,
  author  = {Pavel N. Krivitsky},
  title   = {Using Contrastive Divergence to Seed {Monte} {Carlo} {MLE} for Exponential-family Random Graph Models},
  journal = {Computational Statistics \& Data Analysis},
  year    = {2017},
  volume  = {107},
  pages   = {149--161},
  month   = mar,
  doi     = {10.1016/j.csda.2016.10.015},
}

@Article{KrKu23l,
  author    = {Krivitsky, Pavel N. and Kuvelkar, Alina R. and Hunter, David R.},
  title     = {Likelihood-based Inference for Exponential-Family Random Graph Models via Linear Programming},
  journal   = {Electronic Journal of Statistics},
  year      = {2023},
  volume    = {17},
  number    = {2},
  month     = jan,
  issn      = {1935-7524},
  doi       = {10.1214/23-ejs2176},
  publisher = {Institute of Mathematical Statistics},
}

@article{VaFl15m,
    author = {Vats, Dootika and Flegal, James M. and Jones, Galin L.},
    title = {Multivariate output analysis for {Markov} chain {Monte} {Carlo}},
    journal = {Biometrika},
    volume = {106},
    number = {2},
    pages = {321-337},
    year = {2019},
    month = {04},
    abstract = {Markov chain Monte Carlo produces a correlated sample which may be used for estimating expectations with respect to a target distribution. A fundamental question is: when should sampling stop so that we have good estimates of the desired quantities? The key to answering this question lies in assessing the Monte Carlo error through a multivariate Markov chain central limit theorem. The multivariate nature of this Monte Carlo error has been largely ignored in the literature. We present a multivariate framework for terminating a simulation in Markov chain Monte Carlo. We define a multivariate effective sample size, the estimation of which requires strongly consistent estimators of the covariance matrix in the Markov chain central limit theorem, a property we show for the multivariate batch means estimator. We then provide a lower bound on the number of minimum effective samples required for a desired level of precision. This lower bound does not depend on the underlying stochastic process and can be calculated a priori. This result is obtained by drawing a connection between terminating simulation via effective sample size and terminating simulation using a relative standard deviation fixed-volume sequential stopping rule, which we demonstrate is an asymptotically valid procedure. The finite-sample properties of the proposed method are demonstrated in a variety of examples.},
    doi = {10.1093/biomet/asz002},
}

@Article{WaAt13a,
  author    = {Wang, Jing and Atchad\'{e}, Yves F.},
  title     = {Approximate Bayesian Computation for Exponential Random Graph Models for Large Social Networks},
  journal   = {Communications in Statistics - Simulation and Computation},
  year      = {2013},
  volume    = {43},
  number    = {2},
  pages     = {359--377},
  month     = sep,
  issn      = {1532-4141},
  doi       = {10.1080/03610918.2012.703359},
  publisher = {Informa UK Limited},
}

@Article{Kr12e,
  author   = {Krivitsky, Pavel N.},
  title    = {Exponential-family Random Graph Models for Valued Networks},
  journal  = {Electronic Journal of Statistics},
  year     = {2012},
  volume   = {6},
  pages    = {1100--1128},
  abstract = {Exponential-family random graph models (ERGMs) provide a principled and flexible way to model and simulate features common in social networks, such as propensities for homophily, mutuality, and friend-of-a-friend triad closure, through choice of model terms (sufficient statistics). However, those ERGMs modeling the more complex features have, to date, been limited to binary data: presence or absence of ties. Thus, analysis of valued networks, such as those where counts, measurements, or ranks are observed, has necessitated dichotomizing them, losing information and introducing biases. In this work, we generalize ERGMs to valued networks. Focusing on modeling counts, we formulate an ERGM for networks whose ties are counts and discuss issues that arise when moving beyond the binary case. We introduce model terms that generalize and model common social network features for such data and apply these methods to a network dataset whose values are counts of interactions.},
  doi      = {10.1214/12-EJS696},
}

@Article{KrBu17e,
  author  = {Krivitsky, Pavel N. and Butts, Carter T.},
  title   = {Exponential-family Random Graph Models for Rank-order Relational Data},
  journal = {Sociological Methodology},
  year    = {2017},
  volume  = {47},
  number  = {1},
  pages   = {68--112},
  doi     = {10.1177/0081175017692623},
}

@Article{ShMi05u,
  author   = {Shmueli, Galit and Minka, Thomas P. and Kadane, Joseph B. and Borle, Sharad and Boatwright, Peter},
  title    = {A Useful Distribution for Fitting Discrete Data: Revival of the {Conway--Maxwell--Poisson} Distribution},
  journal  = {Journal of the Royal Statistical Society: Series C},
  year     = {2005},
  volume   = {54},
  number   = {1},
  pages    = {127--142},
  month    = jan,
  issn     = {1467-9876},
  abstract = {A useful discrete distribution (the Conway–Maxwell–Poisson distribution) is revived and its statistical and probabilistic properties are introduced and explored. This distribution is a two-parameter extension of the Poisson distribution that generalizes some well-known discrete distributions (Poisson, Bernoulli and geometric). It also leads to the generalization of distributions derived from these discrete distributions (i.e. the binomial and negative binomial distributions). We describe three methods for estimating the parameters of the Conway–Maxwell–Poisson distribution. The first is a fast simple weighted least squares method, which leads to estimates that are sufficiently accurate for practical purposes. The second method, using maximum likelihood, can be used to refine the initial estimates. This method requires iterations and is more computationally intensive. The third estimation method is Bayesian. Using the conjugate prior, the posterior density of the parameters of the Conway–Maxwell–Poisson distribution is easily computed. It is a flexible distribution that can account for overdispersion or underdispersion that is commonly encountered in count data. We also explore two sets of real world data demonstrating the flexibility and elegance of the Conway–Maxwell–Poisson distribution in fitting count data which do not seem to follow the Poisson distribution.},
  doi      = {10.1111/j.1467-9876.2005.00474.x},
}

@Comment{jabref-meta: databaseType:bibtex;}
