Advertisement

Perfect Sampling

  • Christian P. Robert
  • George Casella
Part of the Springer Texts in Statistics book series (STS)

Abstract

The previous chapters have dealt with methods that are quickly becoming “mainstream”. That is, analyses using Monte Carlo methods in general, and MCMC specifically, are now part of the applied statistician’s tool kit. However, these methods keep evolving, and new algorithms are constantly being developed, with some of these algorithms resulting in procedures that seem radically different from the current standards

Keywords

Markov Chain Acceptance Probability Transition Kernel Slice Sampler Continuous State Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

  1. Casella, G. and Berger, R. (2001). Statistical Inference. Wadsworth, Belmont, CA.Google Scholar
  2. Fismen, M. (1998). Exact simulation using Markov chains. Technical Report 6/98, Institutt for Matematiske Fag, Oslo. Diploma-thesis.Google Scholar
  3. Dimakos, X. K. (2001). A guide to exact simulation. International Statistical Review, 69 (1): 27–48.MathSciNetzbMATHCrossRefGoogle Scholar
  4. Moller, J. and Waagepetersen, R. (2003). Statistical Inference and Simulation for Spatial Point Processes. Chapman and Hall/CRC, Boca Raton.CrossRefGoogle Scholar
  5. Kendall, W. and Moller, J. (2000). Perfect simulation using dominating processes on ordered spaces, with application to locally stable point processes. Advances in Applied Probability, 32: 844–865.MathSciNetzbMATHCrossRefGoogle Scholar
  6. Propp, J. and Wilson, D. (1996). Exact sampling with coupled Markov chains and applications to statistical mechanics. Random Structures and Algorithms, 9: 223–252.MathSciNetzbMATHCrossRefGoogle Scholar
  7. Fernandez, R., Ferrari, P., and Garcia, N. L. (1999). Perfect simulation for interacting point processes, loss networks and Ising models. Technical report, Laboratoire Raphael Salem, Univ. de Rouen.Google Scholar
  8. Berthelsen, K. and Moller, J. (2003). Likelihood and non-parametric Bayesian MCMC inference for spatial point processes based on perfect simulation and path sampling. Scandinavian J. Statist., 30: 549–564.zbMATHCrossRefGoogle Scholar
  9. Marinari, E. and Parisi, G. (1992). Simulated tempering: A new Monte Carlo scheme. Europhys. Lett., 19: 451.CrossRefGoogle Scholar
  10. Geyer, C. and Thompson, E. (1995). Annealing Markov chain Monte Carlo with applications to ancestral inference. J. American Statist. Assoc., 90: 909–920.zbMATHCrossRefGoogle Scholar
  11. Neal, R. (1999). Bayesian Learning for Neural Networks, volume 118. Springer-Verlag, New York. Lecture Notes.Google Scholar
  12. Celeux, G., Hurn, M., and Robert, C. (2000). Computational and inferential difficulties with mixtures posterior distribution. J. American Statist. Assoc., 95 (3): 957–979.MathSciNetzbMATHCrossRefGoogle Scholar
  13. Moller, J. and Nicholls, G. (2004). Perfect simulation for sample-based inference. Statistics and Computing.Google Scholar
  14. Geyer, C. and Thompson, E. (1992). Constrained Monte Carlo maximum likelihood for dependent data (with discussion). J. Royal Statist. Soc. Series B, 54: 657–699.MathSciNetGoogle Scholar
  15. Müller, P. (1999). Simulation based optimal design. In Bernardo, J., Berger, J., Dawid, A., and Smith, A., editors, Bayesian Statistics 6, pages 459–474, New York. Springer-Verlag.Google Scholar
  16. Carlin, B. and Louis, T. (2001). Bayes and Empirical Bayes Methods for Data Analysis. Chapman and Hall, New York, second edition.Google Scholar
  17. Brooks, S., Fan, Y., and Rosenthal, J. (2002). Perfect forward simulation via simulation tempering. Technical report, Department of Statistics, Univ. of Cambridge.Google Scholar

Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Christian P. Robert
    • 1
  • George Casella
    • 2
  1. 1.CEREMADEUniversité Paris DauphineParis Cedex 16France
  2. 2.Department of StatisticsUniversity of FloridaGainesvilleUSA

Personalised recommendations