References
- Arnold, B. C., Castillo, E., and Sarabia, J. M. (2001), “Conditionally Specified Distributions: An Introduction” (with comments and a rejoinder by the authors), Statistical Science, 16, 249–274. DOI: 10.1214/ss/1009213728.
- Athreya, K. B., and Lahiri, S. N. (2006), Measure Theory and Probability Theory, New York: Springer-Verlag.
- Besag, J. (1974), “Spatial Interaction and the Statistical Analysis of Lattice Systems,” Journal of the Royal Statistical Society, Series B, 36, 192–225. DOI: 10.1111/j.2517-6161.1974.tb00999.x.
- Besag, J. (1975), “Statistical Analysis of Non-Lattice Data,” The Statistician, 24, 179–195. DOI: 10.2307/2987782.
- Besag, J. (1977), “Some Methods of Statistical Analysis for Spatial Data,” Bulletin of the International Statistical Institute, 47, 77–92.
- Besag, J., and Green, P. J. (1993), “Spatial Statistics and Bayesian Computation,” Journal of the Royal Statistical Society, Series B, 55, 25–37. DOI: 10.1111/j.2517-6161.1993.tb01467.x.
- Besag, J., York, J., and Mollie, A. (1991), “Bayesian Image Restoration With Two Applications in Spatial Statistics” (with discussion), Annals of the Institute of Statistical Mathematics, 43, 1–59. DOI: 10.1007/BF00116466.
- Brélaz, D. (1979), “New Methods to Color the Vertices of a Graph,” Communications of the ACM, 22, 251–256. DOI: 10.1145/359094.359101.
- Butts, C. T. (2018), “A Perfect Sampling Method for Exponential Family Random Graph Models,” The Journal of Mathematical Sociology, 42, 17–36. DOI: 10.1080/0022250X.2017.1396985.
- Caragea, P. C, and Kaiser, M. S. (2009), “Autologistic Models With Interpretable Parameters,” Journal of Agricultural, Biological, and Environmental Statistics, 14, 281. DOI: 10.1198/jabes.2009.07032.
- Casleton, E., Nordman, D. J., and Kaiser, M. S. (2017), “A Local Structure Model for Network Analysis,” Statistics and Its Interface, 10, 355–367. DOI: 10.4310/SII.2017.v10.n2.a15.
- Chyzh, O. V., and Kaiser, M. S. (2019), “A Local Structure Graph Model: Modeling Formation of Network Edges as a Function of Other Edges,” Political Analysis, in press. DOI: 10.1017/pan.2019.8.
- Cressie, N. (1993), Statistics for Spatial Data: Wiley Series in Probability and Statistics, New York: Wiley.
- Davies, T. M., and Bryant, D. (2013), “On Circulant Embedding for Gaussian Random Fields in R,” Journal of Statistical Software, 55, 1–21. DOI: 10.18637/jss.v055.i09.
- Frank, O., and Strauss, D. (1986), “Markov Graphs,” Journal of the American Statistical Association, 81, 832–842. DOI: 10.1080/01621459.1986.10478342.
- Friel, N., and Pettitt, A. N. (2004), “Likelihood Estimation and Inference for the Autologistic Model,” Journal of Computational and Graphical Statistics, 13, 232–246. DOI: 10.1198/1061860043029.
- Hammersley, J. M., and Clifford, P. (1971), “Markov Fields on Finite Graphs and Lattices,” unpublished.
- Handcock, M. S., bins, G., Snijders, T., Moody, J., and Besag, J. (2003), “Assessing Degeneracy in Statistical Models of Social Networks,” available at http://www.csss.washington.edu/Papers. DOI: 10.1016/j.socnet.2006.08.003.
- Higdon, D. M. (1994), “Spatial Applications of Markov Chain Monte Carlo for Bayesian Inference,” PhD thesis, Department of Statistics, University of Washington, Seattle.
- Higdon, D. M. (1998), “Auxiliary Variable Methods for Markov Chain Monte Carlo With Applications,” Journal of the American Statistical Association, 93, 585–595. DOI: 10.1080/01621459.1998.10473712.
- Hoff, P. D, Raftery, A. E., and Handcock, M. S. (2002), “Latent Space Approaches to Social Network Analysis,” Journal of the American Statistical Association, 97, 1090–1098. DOI: 10.1198/016214502388618906.
- Hughes, J. (2014), “ngspatial: A Package for Fitting the Centered Autologistic and Sparse Spatial Generalized Linear Mixed Models for Areal Data,” The R Journal, 6, 81–95. DOI: 10.32614/RJ-2014-026.
- Hughes, J., Haran, M., and Caragea, P. C. (2011), “Autologistic Models for Binary Data on a Lattice,” Environmetrics, 22, 857–871. DOI: 10.1002/env.1102.
- Hunter, D. R., Handcock, M. S., Butts, C. T., Goodreau, S. M., and Morris, M. (2008), “ergm: A Package to Fit, Simulate and Diagnose Exponential-Family Models for Networks,” Journal of Statistical Software, 24, nihpa54860. DOI: 10.18637/jss.v024.i03.
- Hunziker, P. (2017), “MapColoring: Optimal Contrast Map Coloring,” R Package Version 1.0.
- Hurn, M. (1997), “Difficulties in the Use of Auxiliary Variables in Markov Chain Monte Carlo Methods,” Statistics and Computing, 7, 35–44.
- Husfeldt, T. (2015), “Graph Colouring Algorithms,” in Topics in Chromatic Graph Theory, Encyclopedia of Mathematics and Its Applications, eds. L. W. Beineke and R. J. Wilson, Cambridge: Cambridge University Press, pp. 277–303.
- Jensen, T. R., and Toft, B. (2011), Graph Coloring Problems (Vol. 39), New York: Wiley.
- Johnson, A. A., and Burbank, O. (2015), “Geometric Ergodicity and Scanning Strategies for Two-Component Gibbs Samplers,” Communications in Statistics—Theory and Methods, 44, 3125–3145. DOI: 10.1080/03610926.2013.823209.
- Kaiser, M. S., and Caragea, P. C. (2009), “Exploring Dependence With Data on Spatial Lattices,” Biometrics, 65, 857–865. DOI: 10.1111/j.1541-0420.2008.01118.x.
- Kaiser, M. S., Caragea, P. C., and Furukawa, K. (2012), “Centered Parameterizations and Dependence Limitations in Markov Random Field Models,” Journal of Statistical Planning and Inference, 142, 1855–1863. DOI: 10.1016/j.jspi.2012.02.030.
- Kaiser, M. S., and Cressie, N. (1997), “Modeling Poisson Variables With Positive Spatial Dependence,” Statistics & Probability Letters, 35, 423–432. DOI: 10.1016/S0167-7152(97)00041-2.
- Kaiser, M. S., and Cressie, N. (2000), “The Construction of Multivariate Distributions From Markov Random Fields,” Journal of Multivariate Analysis, 73, 199–220. DOI: 10.1006/jmva.1999.1878.
- Kaiser, M. S., Lahiri, S. N., and Nordman, D. J. (2012), “Goodness of Fit Tests for a Class of Markov Random Field Models,” The Annals of Statistics, 40, 104–130. DOI: 10.1214/11-AOS948.
- Kaiser, M. S., and Nordman, D. J. (2012), “Blockwise Empirical Likelihood for Spatial Markov Model Assessment,” Statistics and Its Interface, 5, 303–318. DOI: 10.4310/SII.2012.v5.n3.a3.
- Kaplan, A. (2019), “Conclique: Gibbs Sampling for Spatial Data and Concliques,” available at https://github.com/andeek/conclique. DOI: 10.1080/10618600.2019.1668800.
- Li, S. Z. (2012), Markov Random Field Modeling in Computer Vision, Japan: Springer Science & Business Media.
- Møller, J. (1999), “Perfect Simulation of Conditionally Specified Models,” Journal of the Royal Statistical Society, Series B, 61, 251–264.
- Møller, J., and Waagepetersen, R. P. (2003), Statistical Inference and Simulation for Spatial Point Processes, Boca Raton, FL: CRC Press.
- Novikov, A. V. (2019), “PyClustering: Data Mining Library,” Journal of Open Source Software, 4, 1230. DOI: 10.21105/joss.01230.
- Propp, J. G., and Wilson, D. B. (1996), “Exact Sampling With Coupled Markov Chains and Applications to Statistical Mechanics,” Random Structures and Algorithms, 9, 223–252. DOI: 10.1002/(SICI)1098-2418(199608/09)9:1/2<223::AID-RSA14>3.0.CO;2-O.
- Roberts, G. O., and Rosenthal, J. S. (2001), “Optimal Scaling for Various Metropolis-Hastings Algorithms,” Statistical Science, 16, 351–367. DOI: 10.1214/ss/1015346320.
- Robins, G., Pattison, P., Kalish, Y., and Lusher, D. (2007), “An Introduction to Exponential Random Graph (P*) Models for Social Networks,” Social Networks, 29, 173–191. DOI: 10.1016/j.socnet.2006.08.002.
- Rue, H. (2001), “Fast Sampling of Gaussian Markov Random Fields,” Journal of the Royal Statistical Society, Series B, 63, 325–338. DOI: 10.1111/1467-9868.00288.
- Rue, H., and Held, L. (2005), Gaussian Markov Random Fields: Theory and Applications, Boca Raton, FL: CRC Press.
- Schweinberger, M., and Handcock, M. S. (2015), “Local Dependence in Random Graph Models: Characterization, Properties and Statistical Inference,” Journal of the Royal Statistical Society, Series B, 77, 647–676. DOI: 10.1111/rssb.12081.
- Snijders, T. A. B., Pattison, P. E., Robins, G. L., and Handcock, M. S. (2006), “New Specifications for Exponential Random Graph Models,” Sociological Methodology, 36, 99–153. DOI: 10.1111/j.1467-9531.2006.00176.x.
- Statisticat, LLC (2016), “LaplacesDemon: Complete Environment for Bayesian Inference,” Bayesian-Inference.com, available at https://web.archive.org/web/20150206004624, http://www.bayesian-inference.com/software.
- Strauss, D., and Ikeda, M. (1990), “Pseudolikelihood Estimation for Social Networks,” Journal of the American Statistical Association, 85, 204–212. DOI: 10.1080/01621459.1990.10475327.
- Swendsen, R. H., and Wang, J.-S. (1987), “Nonuniversal Critical Dynamics in Monte Carlo Simulations,” Physical Review Letters, 58, 86. DOI: 10.1103/PhysRevLett.58.86.
- Turek, D., de Valpine, P., Paciorek, C. J., and Anderson-Bergman, C. (2017), “Automated Parameter Blocking for Efficient Markov Chain Monte Carlo Sampling,” Bayesian Analysis, 12, 465–490. DOI: 10.1214/16-BA1008.
- Wasserman, S., and Pattison, P. (1996), “Logit Models and Logistic Regressions for Social Networks: I. An Introduction to Markov Graphs andp,” Psychometrika, 61, 401–425. DOI: 10.1007/BF02294547.
- Zhang, Y., Brady, M., and Smith, S. (2001), “Segmentation of Brain MR Images Through a Hidden Markov Random Field Model and the Expectation-Maximization Algorithm,” IEEE Transactions on Medical Imaging, 20, 45–57. DOI: 10.1109/42.906424.