Bayesian Model Selection for Exponential Random Graph Models via Adjusted Pseudolikelihoods

References

• Ardia, D., Baştürk, N., Hoogerheide, L., and van Dijk, H. (2012), “A Comparative Study of Monte Carlo Methods for Efficient Evaluation of Marginal Likelihood,” Computational Statistics and Data Analysis, 56, 3398–3414.
   Web of Science ®Google Scholar
• Besag, J. (1972), “Nearest-Neighbour Systems and the Auto-Logistic Model for Binary Data,” Journal of the Royal Statistical Society, Series B, 34, 75–83.
   Google Scholar
• ——— (1975), “Statistical Analysis of Non-Lattice Data,” Statistician, 24, 179–195.
   Google Scholar
• ——— (1977), “Efficiency of Pseudolikelihood Estimation for Simple Gaussian Fields,” Biometrika, 64, 616–618.
   Web of Science ®Google Scholar
• Bouranis, L., Friel, N., and Maire, F. (2017), “Efficient Bayesian Inference for Exponential Random Graph Models by Correcting the Pseudo-Posterior Distribution,” Social Networks, 50, 98–108.
   Web of Science ®Google Scholar
• Caimo, A., and Friel, N. (2011), “Bayesian Inference for Exponential Random Graph Models,” Social Networks, 33, 41–55.
   Web of Science ®Google Scholar
• ——— (2013), “Bayesian Model Selection for Exponential Random Graph Models,” Social Networks, 35, 11–24.
   Web of Science ®Google Scholar
• ——— (2014), “Bergm: Bayesian Exponential Random Graphs in R,” Journal of Statistical Software, 61, 1–25.
   Web of Science ®Google Scholar
• Caimo, A., and Mira, A. (2015), “Efficient Computational Strategies for Doubly Intractable Problems With Applications to Bayesian Social Networks,” Statistics and Computing, 25, 113–125.
   Web of Science ®Google Scholar
• Calderhead, B., and Girolami, M. (2009), “Estimating Bayes Factors via Thermodynamic Integration and Population MCMC,” Computational Statistics and Data Analysis, 53, 4028–4045.
   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., and Jeliazkov, I. (2001), “Marginal Likelihood From the Metropolis-Hastings Output,” Journal of the American Statistical Association, 96, 270–281.
   Web of Science ®Google Scholar
• Del Moral, P., Doucet, A., and Jasra, A. (2006), “Sequential Monte Carlo Samplers,” Journal of the Royal Statistical Society, Series B, 68, 411–436.
   Google Scholar
• Everitt, R., Johansen, A., Rowing, E., and Hogan, M. (2017), “Bayesian Model Selection With Un-Normalised Likelihoods,” Statistics and Computing, 27, 403–422.
   Web of Science ®Google Scholar
• Everitt, R. G. (2012), “Bayesian Parameter Estimation for Latent Markov Random Fields and Social Networks,” Journal of Computational and Graphical Statistics, 24, 940–960.
   Web of Science ®Google Scholar
• Friel, N. (2013), “Evidence and Bayes Factor Estimation for Gibbs Random Fields,” Journal of Computational and Graphical Statistics, 22, 518–532.
   Web of Science ®Google Scholar
• Friel, N., Hurn, M., and Wyse, J. (2014), “Improving Power Posterior Estimation of Statistical Evidence,” Statistics and Computing, 24, 709–723.
   Web of Science ®Google Scholar
• Friel, N., and Pettitt, A. N. (2008), “Marginal Likelihood Estimation via Power Posteriors,” Journal of the Royal Statistical Society, Series B, 70, 589–607.
   Google Scholar
• Friel, N., and Rue, H. (2007), “Recursive Computing and Simulation-Free Inference for General Factorizable Models,” Biometrika, 93, 661–672.
   Web of Science ®Google Scholar
• Friel, N., and Wyse, J. (2012), “Estimating the Evidence - A Review,” Statistica Neerlandica, 66, 288–308.
   Web of Science ®Google Scholar
• Gelman, A., and Meng, X. (1998), “Simulating Normalizing Constants: From Importance Sampling to Bridge Sampling to Path Sampling,” Statistical Science, 13, 163–185.
   Web of Science ®Google Scholar
• Geyer, C., and Thompson, E. (1992), “Constrained Monte Carlo Maximum Likelihood for Dependent Data” (with discussion) Journal of the Royal Statistical Society, Series B, 54, 657–699.
   Google Scholar
• Hunter, D., and Handcock, M. (2006), “Inference in Curved Exponential Family Models for Networks,” Journal of Computational and Graphical Statistics, 15, 565–583.
   Web of Science ®Google Scholar
• Hunter, D., Handcock, M., Butts, C., Goodreau, S., and Morris, M., (2008), “ergm: A Package to Fit, Simulate and Diagnose Exponential-Family Models for Networks,” Journal of Computational and Graphical Statistics, 24, 1–29.
   Google Scholar
• Kass, R. E., and Raftery, A. E. (1995), “Bayes Factors,” Journal of the American Statistical Association, 90, 773–795.
   Web of Science ®Google Scholar
• Koskinen, J. (2004), “Bayesian Analysis of Exponential Random Graphs - Estimation of Parameters and Model Selection,” Technical Report 2, Department of Statistics, Stockholm University.
   Google Scholar
• Lartillot, N., and Phillipe, H. (2006), “Computing Bayes Factors Using Thermodynamic Integration,” Systematic Biology, 55, 195–207.
   PubMed Web of Science ®Google Scholar
• Lindsay, B. G. (1988), “Composite Likelihood Methods,” Contemporary Mathematics, 80, 221–239.
   Google Scholar
• Liu, J. (2001), Monte Carlo Strategies in Scientific Computing, New York: Springer Publishing Company, Incorporated.
   Google Scholar
• Martin, A., Quinn, K., and Park, J. (2011), “MCMCpack: Markov Chain Monte Carlo in R,” Journal of Statistical Software, 42, 22.
   Web of Science ®Google Scholar
• Meng, X., and Wong, W. H. (1996), “Simulating Ratios of Normalizing Constants via a Simple Identity: A Theoretical Exploration,” Statistica Sinica, 6, 831–860.
   Web of Science ®Google Scholar
• Møller, J., Pettit, A., Reeves, R., and Bertheksen, K. (2006), “An Efficient Markov Chain Monte Carlo Method for Distributions With Intractable Normalising Constants,” Biometrika, 93, 451–458.
   Web of Science ®Google Scholar
• Morris, M., Handcock, M., and Hunter, D. (2008), “Specification of Exponential-Family Random Graph Models: Terms and Computational Aspects,” Journal of Statistical Software, 24, 1–24.
   PubMedGoogle Scholar
• Neal, R. (2001), “Annealed Importance Sampling,” Statistics and Computing, 11, 125–139.
   Web of Science ®Google Scholar
• Oates, C., Papamarkou, T., and Girolami, M. (2016), “The Controlled Thermodynamic Integral for Bayesian Model Evidence Evaluation,” Journal of the American Statistical Association, 111, 634–645.
   Web of Science ®Google Scholar
• Pearson, M., and Michell, L. (2000), “Smoke Rings: Social Network Analysis of Friendship Groups, Smoking and Drug-Taking,” Drugs: Education, Prevention and Policy, 7, 21–37.
   Web of Science ®Google Scholar
• Potts, R. B. (1952), “Some Generalized Order-Disorder Transformations,” Proceedings of the Cambridge Philosophical Society, 48, 106–109.
   Web of Science ®Google Scholar
• R Core Team (2017), R: A Language and Environment for Statistical Computing, Vienna, Austria: R Foundation for Statistical Computing.
   Google Scholar
• Reeves, R., and Pettitt, A. N. (2004), “Efficient Recursions for General Factorisable Models,” Biometrika, 91, 751–757.
   Web of Science ®Google Scholar
• Ribatet, M., Cooley, D., and Davison, A. (2012), “Bayesian Inference From Composite Likelihoods, With an Application to Spatial Extremes,” Statistica Sinica, 22, 813–845.
   Web of Science ®Google Scholar
• Robins, G., Snijders, T., Wang, P., Handcock, M., and Pattison, P. (2007), “Recent Developments in Exponential Random Graph (p*) Models for Social Networks,” Social Networks, 29, 192–215.
   Web of Science ®Google Scholar
• Rosenthal, J., and Roberts, G. (2001), “Optimal Scaling for Various Metropolis-Hastings Algorithms,” Statistical Science, 16, 351–367.
   Web of Science ®Google Scholar
• Snijders, T., Pattison, P., Robins, G., and Handcock, M. (2006), “New Specifications for Exponential Random Graph Models,” Sociological Methodology, 36, 99–153.
   Web of Science ®Google Scholar
• Stoehr, J., and Friel, N. (2015), “Calibration of Conditional Composite Likelihood for Bayesian Inference on Gibbs Random Fields,” AISTATS, Journal of Machine Learning Research: W & CP, 38, pp. 921–929.
   Google Scholar
• Stoehr, J., Pudlo, P., and Friel, N. (2016), GiRaF: Gibbs Random Fields Analysis, R Package Version 1.0.
   Google Scholar
• Strauss, D., and Ikeda, M. (1990), “Pseudolikelihood Estimation for Social Networks,” Journal of the American Statistical Association, 85, 204–212.
   Web of Science ®Google Scholar
• Thiemichen, S., Friel, N., Caimo, A., and Kauermann, G. (2016), “Bayesian Exponential Random Graph Models With Nodal Random Effects,” Social Networks, 46, 11–28.
   Web of Science ®Google Scholar
• Varin, C., Reid, N., and Firth, D. (2011), “An Overview of Composite Likelihood Methods,” Statistica Sinica, 21, 5–42.
   Web of Science ®Google Scholar
• Wang, J., and Atchade, Y. F. (2014), “Bayesian Inference of Exponential Random Graph Models for Large Social Networks,” Communications in Statistics - Simulation and Computation, 43, 359–377.
   Web of Science ®Google Scholar
• Wasserman, S., and Pattison, P. (1996), “Logit Models and Logistic Regression for Social Networks: I. An Introduction to Markov Graphs and p*,” Psychometrica, 61, 401–425.
   Web of Science ®Google Scholar
• Xie, W., Lewis, P. O., Fan, Y., Kuo, L., and Chen, M. (2011), “Improving Marginal Likelihood Estimation for Bayesian Phylogenetic Model Selection,” Systematic Biology, 60, 150–160.
   PubMed Web of Science ®Google Scholar