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Theory and Methods

An Adaptive Exchange Algorithm for Sampling From Distributions With Intractable Normalizing Constants

Pages 377-393 | Received 01 Oct 2013, Published online: 05 May 2016

REFERENCES

  • Andrews, D., and Herzberg, A. (1985), Data, New York: Springer.
  • Andrieu, C., Doucet, A., and Holenstein, R. (2010), Particle Markov Chain Monte Carlo Methods, Journal of the Royal Statistical Society, Series B, 72, 269–342.
  • Andrieu, C., and Moulines, E. (2006), On the Ergodicity Properties of Some Adaptive MCMC Algorithms, Annals of Applied Probability, 16, 1462–1505.
  • Andrieu, C., Moulines, E., and Priouret, P. (2005), Stability of Stochastic Approximation Under Verifiable Conditions, SIAM Journal of Control and Optimization, 44, 283–312.
  • Andrieu, C., and Roberts, G. (2009), The Pseudo-Marginal Approach for Efficient Monte Carlo Computations, Annals of Statistics, 37, 697–725.
  • Atchade, Y.F., Lartillot, N., and Robert, C.P. (2013), Bayesian Computation for Intractable Normalizing Constants, Brazilian Journal of Statistics, 27, 416–436.
  • Atchade, Y.F., and Liu, J.S. (2010), The Wang-Landau Algorithm in General State Spaces: Applications and Convergence Analysis, Statistica Sinica, 20, 209–233.
  • Balram, N., and Moura, J. (1993), Noncausal Gauss Markov Random Fields: Parameter Structure and Estimation, IEEE Transactions on Information Theory, 39, 1333–1355.
  • Beaumont, M.A., Zhang, W., and Balding, D.J. (2002), Approximate Bayesian Computation in Population Genetics, Genetics, 162, 2025–2035.
  • Besag, J.E. (1974), Spatial Interaction and the Statistical Analysis of Lattice Systems” (), Journal of the Royal Statistical Society, Series B, 36, 192–236.
  • Besag, J.E., and Moran, P. (1975), On the Estimation and Testing of Spatial Interaction in Gaussian Lattice Processes, Biometrika, 62, 555–562.
  • Caimo, A., and Friel, N. (2011), Bayesian Inference for Exponential Random Graph Models, Social Networks, 33, 41–55.
  • Chang, M. (2011), Modern Issues and Methods in Biostatistics, New York: Springer.
  • Childs, A.M., Patterson, R.B., and MacKay, D.J. (2001), Exact Sampling From Non-Attractive Distributions Using Summary States, Physics Review E, 63, 036113.
  • Everitt, R.G. (2012), Bayesian Parameter Estimation for Latent Markov Random Fields and Social Networks, Journal of Computational and Graphical Statistics, 21, 940–960.
  • Ferguson, T.S. (1996), A Course in Large Sample Theory, New York: Chapman & Hall.
  • Fort, G., Moulines, E., and Priouret, P. (2011), Convergence of Adaptive and Interacting Markov Chain Monte Carlo Algorithms, Annals of Statistics, 39, 3262–3289.
  • Gelman, A., and Rubin, D. (1992), Inference From Iterative Simulation Using Multiple Sequences (, Statistical Science, 7, 457–511.
  • Geyer, C. J. (1991), “Markov Chain Monte Carlo Maximum Likelihood,” in Computer Science and Statistics: Proceedings of the 23rd Symposium on the Interface, eds. E. Keramidas and S. M. Kauffman, Fairfax Station, VA: Interface Foundation, pp. 156–163.
  • 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.
  • Green, P.J. (1995), Reversible Jump Markov Chain Monte Carlo Computation and Bayesian Model Determination, Biometrika, 82, 711–732.
  • Gu, M., and Zhu, H. (2001), Maximum Likelihood Estimation for Spatial Models by Markov Chain Monte Carlo Stochastic Approximation, Journal of the Royal Statistical Society, Series B, 63, 339–355.
  • Haario, H., Saksman, E., and Tamminen, J. (2001), An Adaptive Metropolis Algorithm, Bernoulli, 7, 223–242.
  • Huang, F., and Ogata, Y. (1999), Improvements of the Maximum Pesudo-Likelihood Estimators in Various Spatial Statistical Models, Journal of Computational and Graphical Statistics, 8, 510–530.
  • Hukushima, K., and Nemoto, K. (1996), Exchange Monte Carlo Method and Application to Spin Glass Simulations, Journal of the Physical Society of Japan, 65, 1604–1608.
  • Hurn, M. A., Husby, O. K., and Rue, H. (2003), “A Tutorial on Image Analysis,” in Spatial Statistics and Computational Methods: Lecture Notes in Statistics (Vol. 173), New York: Springer, pp. 87–141.
  • Jin, I.H., and Liang, F. (2014), Use of SAMC for Bayesian Analysis of Statistical Models With Intractable Normalizing Constants, Computational Statistics and Data Analysis, 71, 402–416.
  • Liang, F. (2007), Continuous Contour Monte Carlo for Marginal Density Estimation With an Application to a Spatial Statistical Models, Journal of Computational and Graphical Statistics, 16, 608–632.
  • ——— (2009), Improving SAMC Using Smoothing Methods: Theory and Applications to Bayesian Model Selection Problems, Annals of Statistics, 37, 2626–2654.
  • ——— (2010), A Double Metropolis-Hastings Sampler for Spatial Models With Intractable Normalizing Constants, Journal of Statistical Computing and Simulation, 80, 1007–1022.
  • Liang, F., and Jin, I.H. (2013), A Monte Carlo Metropolis-Hastings Algorithm for Sampling From Distributions With Intractable Normalizing Constants, Neural Computation, 25, 2199–2234.
  • Liang, F., Liu, C., and Carroll, R.J. (2007), Stochastic Approximation in Monte Carlo Computation, Journal of American Statistical Association, 102, 305–320.
  • ——— (2010), Advanced Markov Chain Monte Carlo Methods: Learning from Past Samples, Chichester: Wiley.
  • Liang, F., and Wong, W.H. (2001), Real-Parameter Evolutionary Sampling With Applications in Bayesian Mixture Models, Journal of the American Statistical Association, 96, 653–666.
  • Lin, F. (2014), Split-and-Merge Strategies for Big Data Analysis, Ph.D dissertation, Department of Statistics, Texas A&M University.
  • Lyne, A., Girolami, M., Atchade, Y., Strathmann, H., and Simpson, D. (2014), Playing Russian Roulette With Intractable Likelihoods, arXv:1306.4032v2.
  • Martin, R., Zhang, J. and Liu, C.2010
  • Møller, J., Pettitt, A.N., Reeves, R.W., and Berthelsen, K.K. (2006), An Efficient Markov Chain Monte Carlo Method for Distributions With Intractable Normalising Constants, Biometrika, 93, 451–459.
  • Murray, I., Ghahramani, Z., and MacKay, D. J. (2006), “MCMC for Doubly-Intractable Distributions,” in Proceedings of 22nd Annual Conference on Uncertainty in Artificial Intelligence (UAI), eds. R. Dechter and T. S. Richardson, Cambridge, MA: AUAI Press, pp. 359–366.
  • Neal, R. (1998), Annealed Importance Sampling, Statistics and Computing, 11, 125–139.
  • Plummer, M., Best, N., Cowles, K., Vines, K., Sarkar, D., Almond, R. (2012), Coda: Output Analysis and Diagnostics for Markov Chain Monte Carlo Simulations, R Package. Available at http://cran.r–project.org
  • Preisler, H.K. (1993), Modeling Spatial Patterns of Trees Attacked by Bark-Beetles, Applied Statistics, 42, 501–514.
  • 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.
  • Riggan, W. B., Creason, J. P., Nelson, W. C., Manton, K. G., Woodbury, M. A., Stallard, E., Pellom, A. C., and Beaubier, J. (1987), U.S. Cancer Mortality Rates and Trends, 1950–1979 (Vol. IV: Maps), Washington, D.C.: U.S. Government Printing Office.
  • Roberts, G.O., and Rosenthal, J.S. (2007), Coupling and Ergodicity of Adaptive Markov Chain Monte Carlo Algorithms, Journal of Applied Probability, 44, 458–475.
  • Roberts, G.O., and Tweedie, R.L. (1996), Geometric Convergence and Central Limit Theorems for Multidimensional Hastings and Metropolis Algorithms, Biometrika, 83, 95–110.
  • Rosenthal, J.S. (1995), Minorization Conditions and Convergence Rate for Markov Chain Monte Carlo, Journal of American Statistical Association, 90, 558–566.
  • Sherman, M., Apanasovich, T.V., and Carroll, R.J. (2006), On Estimation in Binary Autologistic Spatial Models, Journal of Statistical Computation and Simulation, 76, 167–179.
  • Snijders, T.A., Pattison, P.E., Robins, G.L., and Handcock, M.S. (2006), New Specification for Exponential Random Graph Models, Sociological Methodology, 36, 99–153.

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