A Function Emulation Approach for Doubly Intractable Distributions

References

• Alquier, P., Friel, N., Everitt, R., and Boland, A. (2016), “Noisy Monte Carlo: Convergence of Markov Chains With Approximate Transition Kernels,” Statistics and Computing, 26, 29–47. DOI: 10.1007/s11222-014-9521-x.
   Web of Science ®Google Scholar
• Andrieu, C., and Roberts, G. O. (2009), “The Pseudo-Marginal Approach for Efficient Monte Carlo Computations,” The Annals of Statistics, 37, 697–725. DOI: 10.1214/07-AOS574.
   Web of Science ®Google Scholar
• Atchade, Y., Lartillot, N., and Robert, C. P. (2008), “Bayesian Computation for Statistical Models With Intractable Normalizing Constants,” Brazilian Journal of Probability and Statistics, 27, 416–436. DOI: 10.1214/11-BJPS174.
   Google Scholar
• Beaumont, M. A. (2003), “Estimation of Population Growth or Decline in Genetically Monitored Populations,” Genetics, 164, 1139–1160.
   PubMed Web of Science ®Google Scholar
• Beaumont, M. A., Zhang, W., and Balding, D. J. (2002), “Approximate Bayesian Computation in Population Genetics,” Genetics, 162, 2025–2035.
   PubMed Web of Science ®Google Scholar
• Besag, J. (1974), “Spatial Interaction and the Statistical Analysis of Lattice Systems,” Journal of the Royal Statistical Society, Series B, 36, 192–236. DOI: 10.1111/j.2517-6161.1974.tb00999.x.
   Google Scholar
• Bliznyuk, N., Ruppert, D., and Shoemaker, C. A. (2012), “Local Derivative-Free Approximation of Computationally Expensive Posterior Densities,” Journal of Computational and Graphical Statistics, 21, 476–495. DOI: 10.1080/10618600.2012.681255.
   Web of Science ®Google Scholar
• Boland, A., Friel, N., and Maire, F. (2017), “Efficient MCMC for Gibbs Random Fields Using Pre-Computation,” arXiv no. 1710.04093.
   Google Scholar
• Christen, J. A., and Fox, C. (2005), “Markov Chain Monte Carlo Using an Approximation,” Journal of Computational and Graphical Statistics, 14, 795–810. DOI: 10.1198/106186005X76983.
   Web of Science ®Google Scholar
• Conrad, P. R., Marzouk, Y. M., Pillai, N. S., and Smith, A. (2016), “Accelerating Asymptotically Exact MCMC for Computationally Intensive Models via Local Approximations,” Journal of the American Statistical Association, 111, 1591–1607. DOI: 10.1080/01621459.2015.1096787.
   Web of Science ®Google Scholar
• Cressie, N. (2015), Statistics for Spatial Data, New York: Wiley.
   Google Scholar
• Dagum, L., and Menon, R. (1998), “OpenMP: An Industry Standard API for Shared-Memory Programming,” IEEE Computational Science and Engineering, 5, 46–55. DOI: 10.1109/99.660313.
   Web of Science ®Google Scholar
• Dietz, K. (1967), “Epidemics and Rumours: A Survey,” Journal of the Royal Statistical Society, Series A, 130, 505–528. DOI: 10.2307/2982521.
   Google Scholar
• Drovandi, C. C., Moores, M. T., and Boys, R. J. (2018), “Accelerating Pseudo-Marginal MCMC Using Gaussian Processes,” Computational Statistics & Data Analysis, 118, 1–17. DOI: 10.1016/j.csda.2017.09.002.
   Web of Science ®Google Scholar
• Eddelbuettel, D., François, R., Allaire, J., Chambers, J., Bates, D., and Ushey, K. (2011), “Rcpp: Seamless R and C++ Integration,” Journal of Statistical Software, 40, 1–18. DOI: 10.18637/jss.v040.i08.
   Web of Science ®Google Scholar
• Flegal, J. M., Haran, M., and Jones, G. L. (2008), “Markov Chain Monte Carlo: Can We Trust the Third Significant Figure?,” Statistical Science, 23, 250–260. DOI: 10.1214/08-STS257.
   Web of Science ®Google Scholar
• Geyer, C. J. (2011), “Introduction to Markov Chain Monte Carlo,” in Handbook of Markov Chain Monte Carlo, eds. S. Brooks, A. Gelman, X.-L. Meng, and G. L. Jones, Boca Raton, FL: Chapman & Hall.
   Google Scholar
• Geyer, C. J., and Møller, J. (1994), “Simulation Procedures and Likelihood Inference for Spatial Point Processes,” Scandinavian Journal of Statistics, 21, 359–373.
   Web of Science ®Google Scholar
• Geyer, C. J., and Thompson, E. A. (1992), “Constrained Monte Carlo Maximum Likelihood for Dependent Data,” Journal of the Royal Statistical Society, Series B, 54, 657–699. DOI: 10.1111/j.2517-6161.1992.tb01443.x.
   Google Scholar
• Goldstein, J., Haran, M., Simeonov, I., Fricks, J., and Chiaromonte, F. (2015), “An Attraction-Repulsion Point Process Model for Respiratory Syncytial Virus Infections,” Biometrics, 71, 376–385. DOI: 10.1111/biom.12267.
   PubMed Web of Science ®Google Scholar
• Golightly, A., Henderson, D. A., and Sherlock, C. (2015), “Delayed Acceptance Particle MCMC for Exact Inference in Stochastic Kinetic Models,” Statistics and Computing, 25, 1039–1055. DOI: 10.1007/s11222-014-9469-x.
   Web of Science ®Google Scholar
• Gramacy, R. B., and Apley, D. W. (2015), “Local Gaussian Process Approximation for Large Computer Experiments,” Journal of Computational and Graphical Statistics, 24, 561–578. DOI: 10.1080/10618600.2014.914442.
   Web of Science ®Google Scholar
• Gramacy, R. B., and Lee, H. K. (2008), “Bayesian Treed Gaussian Process Models With an Application to Computer Modeling,” Journal of the American Statistical Association, 103, 1119–1130. DOI: 10.1198/016214508000000689.
   Web of Science ®Google Scholar
• Gutmann, M. U., and Corander, J. (2016), “Bayesian Optimization for Likelihood-Free Inference of Simulator-Based Statistical Models,” The Journal of Machine Learning Research, 17, 4256–4302.
   Web of Science ®Google Scholar
• Hughes, J., Haran, M., and Caragea, P. (2011), “Autologistic Models for Binary Data on a Lattice,” Environmetrics, 22, 857–871. DOI: 10.1002/env.1102.
   Web of Science ®Google Scholar
• Hunter, D. R. (2007), “Curved Exponential Family Models for Social Networks,” Social Networks, 29, 216–230. DOI: 10.1016/j.socnet.2006.08.005.
   PubMed Web of Science ®Google Scholar
• Hunter, D. R., and Handcock, M. S. (2006), “Inference in Curved Exponential Family Models for Networks,” Journal of Computational and Graphical Statistics, 15, 565–583. DOI: 10.1198/106186006X133069.
   Web of Science ®Google Scholar
• 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.
   PubMedGoogle Scholar
• Ihaka, R., and Gentleman, R. (1996), “R: A Language for Data Analysis and Graphics,” Journal of Computational and Graphical Statistics, 5, 299–314. DOI: 10.1080/10618600.1996.10474713.
   Google Scholar
• Järvenpää, M., Gutmann, M., Vehtari, A., and Marttinen, P. (2016), “Gaussian Process Modeling in Approximate Bayesian Computation to Estimate Horizontal Gene Transfer in Bacteria,” arXiv no. 1610.06462.
   Google Scholar
• Jin, I. H., Yuan, Y., and Liang, F. (2013), “Bayesian Analysis for Exponential Random Graph Models Using the Adaptive Exchange Sampler,” Statistics and Its Interface, 6, 559. DOI: 10.4310/SII.2013.v6.n4.a13.
   PubMed Web of Science ®Google Scholar
• Jones, G. L., Haran, M., Caffo, B. S., and Neath, R. (2006), “Fixed-Width Output Analysis for Markov Chain Monte Carlo,” Journal of the American Statistical Association, 101, 1537–1547. DOI: 10.1198/016214506000000492.
   Web of Science ®Google Scholar
• Joseph, V. R. (2012), “Bayesian Computation Using Design of Experiments-Based Interpolation Technique,” Technometrics, 54, 209–225. DOI: 10.1080/00401706.2012.680399.
   Web of Science ®Google Scholar
• Joseph, V. R., Dasgupta, T., Tuo, R., and Wu, C. J. (2015), “Sequential Exploration of Complex Surfaces Using Minimum Energy Designs,” Technometrics, 57, 64–74. DOI: 10.1080/00401706.2014.881749.
   Web of Science ®Google Scholar
• Kass, R. E., Carlin, B. P., Gelman, A., and Neal, R. M. (1998), “Markov Chain Monte Carlo in Practice: A Roundtable Discussion,” The American Statistician, 52, 93–100. DOI: 10.1080/00031305.1998.10480547.
   Web of Science ®Google Scholar
• Kennedy, M. C., and O’Hagan, A. (2001), “Bayesian Calibration of Computer Models,” Journal of the Royal Statistical Society, Series B, 63, 425–464. DOI: 10.1111/1467-9868.00294.
   Web of Science ®Google Scholar
• Krige, D. G. (1951), “A Statistical Approach to Some Basic Mine Valuation Problems on the Witwatersrand,” Journal of Chemical, Metallurgical, and Mining Society of South Africa, 52, 119–139.
   Google Scholar
• Liang, F. (2010), “A Double Metropolis–Hastings Sampler for Spatial Models With Intractable Normalizing Constants,” Journal of Statistical Computation and Simulation, 80, 1007–1022. DOI: 10.1080/00949650902882162.
   Web of Science ®Google Scholar
• Liang, F., Jin, I. H., Song, Q., and Liu, J. S. (2016), “An Adaptive Exchange Algorithm for Sampling From Distributions With Intractable Normalizing Constants,” Journal of the American Statistical Association, 111, 377–393. DOI: 10.1080/01621459.2015.1009072.
   Web of Science ®Google Scholar
• Lyne, A.-M., Girolami, M., Atchade, Y., Strathmann, H., and Simpson, D. (2015), “On Russian Roulette Estimates for Bayesian Inference With Doubly-Intractable Likelihoods,” Statistical Science, 30, 443–467. DOI: 10.1214/15-STS523.
   Web of Science ®Google Scholar
• Marin, J.-M., Pudlo, P., Robert, C. P., and Ryder, R. J. (2012), “Approximate Bayesian Computational Methods,” Statistics and Computing, 22, 1167–1180. DOI: 10.1007/s11222-011-9288-2.
   Web of Science ®Google Scholar
• Marjoram, P., Molitor, J., Plagnol, V., and Tavaré, S. (2003), “Markov Chain Monte Carlo Without Likelihoods,” Proceedings of the National Academy of Sciences of the United States of America, 100, 15324–15328. DOI: 10.1073/pnas.0306899100.
   PubMed Web of Science ®Google Scholar
• Marzouk, Y., and Xiu, D. (2009), “A Stochastic Collocation Approach to Bayesian Inference in Inverse Problems,” Communications in Computational Physics, 6, 826–847. DOI: 10.4208/cicp.2009.v6.p826.
   Web of Science ®Google Scholar
• Marzouk, Y. M., Najm, H. N., and Rahn, L. A. (2007), “Stochastic Spectral Methods for Efficient Bayesian Solution of Inverse Problems,” Journal of Computational Physics, 224, 560–586. DOI: 10.1016/j.jcp.2006.10.010.
   Web of Science ®Google Scholar
• Meeds, E., and Welling, M. (2014), “GPS-ABC: Gaussian Process Surrogate Approximate Bayesian Computation,” in Proceedings of the 30th Conference on Uncertainty in Artificial Intelligence, pp. 593–602.
   Google Scholar
• Mitrophanov, A. Y. (2005), “Sensitivity and Convergence of Uniformly Ergodic Markov Chains,” Journal of Applied Probability, 42, 1003–1014. DOI: 10.1239/jap/1134587812.
   Web of Science ®Google Scholar
• Møller, J., Pettitt, A. N., Reeves, R., and Berthelsen, K. K. (2006), “An Efficient Markov Chain Monte Carlo Method for Distributions With Intractable Normalising Constants,” Biometrika, 93, 451–458. DOI: 10.1093/biomet/93.2.451.
   Web of Science ®Google Scholar
• Moores, M. T., Drovandi, C. C., Mengersen, K., and Robert, C. P. (2015), “Pre-Processing for Approximate Bayesian Computation in Image Analysis,” Statistics and Computing, 25, 23–33. DOI: 10.1007/s11222-014-9525-6.
   Web of Science ®Google Scholar
• Murray, I., Ghahramani, Z., and MacKay, D. J. C. (2006), “MCMC for Doubly-Intractable Distributions,” in Proceedings of the 22nd Annual Conference on Uncertainty in Artificial Intelligence (UAI-06), AUAI Press, pp. 359–366.
   Google Scholar
• Park, J., Goldstein, J., Haran, M., and Ferrari, M. (2017), “An Ensemble Approach to Predicting the Impact of Vaccination on Rotavirus Disease in Niger,” Vaccine, 35, 5835–5841. DOI: 10.1016/j.vaccine.2017.09.020.
   PubMed Web of Science ®Google Scholar
• Park, J., and Haran, M. (2018), “Bayesian Inference in the Presence of Intractable Normalizing Functions,” Journal of the American Statistical Association, 113, 1372–1390. DOI: 10.1080/01621459.2018.1448824.
   Web of Science ®Google Scholar
• 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.
   Web of Science ®Google Scholar
• Rasmussen, C. E. (2004), “Gaussian Processes in Machine Learning,” in Advanced Lectures on Machine Learning, Berlin, Heidelberg: Springer, pp. 63–71.
   Google Scholar
• Reich, B. J., and Gardner, B. (2014), “A Spatial Capture-Recapture Model for Territorial Species,” Environmetrics, 25, 630–637. DOI: 10.1002/env.2317.
   Web of Science ®Google Scholar
• Resnick, M. D., Bearman, P. S., Blum, R. W., Bauman, K. E., Harris, K. M., Jones, J., Tabor, J., Beuhring, T., Sieving, R. E., Shew, M., and Ireland, M. (1997), “Protecting Adolescents From Harm: Findings From the National Longitudinal Study on Adolescent Health,” Jama, 278, 823–832.
   PubMed Web of Science ®Google Scholar
• Robert, C., and Casella, G. (2013), Monte Carlo Statistical Methods, New York: Springer Science & Business Media.
   Google Scholar
• 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.
   Web of Science ®Google Scholar
• Roustant, O., Ginsbourger, D., and Deville, Y. (2012), “DiceKriging, DiceOptim: Two R Packages for the Analysis of Computer Experiments by Kriging-Based Metamodeling and Optimization,” Journal of Statistical Software, 51, 1–55. DOI: 10.18637/jss.v051.i01.
   PubMed Web of Science ®Google Scholar
• Sacks, J., Welch, W. J., Mitchell, T. J., and Wynn, H. P. (1989), “Design and Analysis of Computer Experiments,” Statistical Science, 4, 409–423. DOI: 10.1214/ss/1177012413.
   Google Scholar
• Sherlock, C., Golightly, A., and Henderson, D. A. (2017), “Adaptive, Delayed-Acceptance MCMC for Targets With Expensive Likelihoods,” Journal of Computational and Graphical Statistics, 26, 434–444. DOI: 10.1080/10618600.2016.1231064.
   Web of Science ®Google Scholar
• Strauss, D. J. (1975), “A Model for Clustering,” Biometrika, 62, 467–475. DOI: 10.1093/biomet/62.2.467.
   Web of Science ®Google Scholar
• Torrie, G. M., and Valleau, J. P. (1977), “Nonphysical Sampling Distributions in Monte Carlo Free-Energy Estimation: Umbrella Sampling,” Journal of Computational Physics, 23, 187–199. DOI: 10.1016/0021-9991(77)90121-8.
   Web of Science ®Google Scholar
• Wang, H., and Li, J. (2017), “Adaptive Gaussian Process Approximation for Bayesian Inference With Expensive Likelihood Functions,” arXiv no. 1703.09930.
   Google Scholar
• Wilkinson, R. D. (2014), “Accelerating ABC Methods Using Gaussian Processes,” JMLR Workshop and Conference Proceedings, 33, 1015–1023.
   Google Scholar