Skip to main content

Part of the book series: Lecture Notes in Statistics ((LNS,volume 67))

  • 414 Accesses

Abstract

To motivate the Gibbs Sampler, we consider a modification of Data Augmentation which we will refer to as Chained Data Augmentation. The Gibbs Sampler turns out to be a multivariate extension of Chained Data Augmentation.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 74.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Besag, J. (1974). “Spatial Interaction and the Statistical Analysis of Lattice Systems”, Journal of the Royal Statistical Society, B., 36, 192–326.

    MathSciNet  MATH  Google Scholar 

  • Carlin, B.P., Gelfand, A.E. and Smith, A.P.M. (1990). “Hierarchical Bayesian Analysis of Change Point Problems”, Technical Report.

    Google Scholar 

  • Carlin, B.P., and Poison, N.G. (1990a). “An Expected Utility Approach to Influence Diagnostics”, Technical Report.

    Google Scholar 

  • Carlin, B.P., and Poison, N.G. (1990b). “Bayesian Model Choice in Nonconjugate Settings”, Technical Report.

    Google Scholar 

  • Carlin, B.P., Poison, N.G. and Stoffer, D.S. (1990). “A Monte Carlo Approach to Nonnormal and Nonlinear State Space Modeling”, Technical Report.

    Google Scholar 

  • Carlin, B.P. and Schervish, M. (1990). “Monitoring the Convergence of the Gibbs Samplers”Technical Report.

    Google Scholar 

  • Gelfand, A.E., Hills, S.B., Racine-Poon, A. and Smith, A.F.M. (1990). “Illustration of Bayesian Inference in Normal Data Models Using Gibbs Sampling”, Technical Report.

    Google Scholar 

  • Gelfand, A.E. and Smith, A.F.M. (1990a). “Sampling Based Approaches to Calculating Marginal Densities”, Journal of the American Statistical Association, 85, 398–409.

    MathSciNet  MATH  Google Scholar 

  • Gelfand, A.E. and Smith, A.F.M. (1990b). “Gibbs Sampling for Marginal Posterior Expectations”, Technical Report.

    Google Scholar 

  • Gelfand, A.E., Smith, A.F.M. and Lee, T.M. (1990). “Bayesian Analysis of Constrained Parameter and Truncated Data Problems”, Technical Report.

    Google Scholar 

  • Geman, S. and Geman, D. (1984). “Stochastic Relaxation, Gibbs Distribution and the Bayesian Restoration of Images”, IEEE Transactions on Pattern Analysis and Machine Intelligence, 6, 721–741.

    Google Scholar 

  • Hasting, W.K. (1970). “Monte Carlo Sampling Methods Using Markov Chains and Their Applications”, Biometrika, 57, 97–109.

    Article  Google Scholar 

  • Li, K.H. (1985). PhD Thesis, University of Chicago.

    Google Scholar 

  • Li, K.H. (1988). “Imputation Using Markov Chains”, Journal of Statistical Computation and Simulation, 30, 57–79,

    Article  MathSciNet  MATH  Google Scholar 

  • McCullagh, P. and Nelder, J. (1989). Generalized Linear Models, London: Chapman and Hall.

    MATH  Google Scholar 

  • Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H., and Teller, E. (1953). “Equations of State Calculations by Fast Computing Machines”, Journal of Chemical Physics, 21, 1087–1091.

    Google Scholar 

  • Monis, C. (1987). Comment on “The Calculation of Posterior Distributions by Data Augmentation”, Journal of the American Statistical Assocition, 82, 542–543.

    Google Scholar 

  • Ripley, B. (1987). Stochastic Simulation, New York: Wiley.

    Book  MATH  Google Scholar 

  • Ritter, C. and Tanner, M.A. (1990). “The Griddy Gibbs Sampler”, Technical-Report.

    Google Scholar 

  • Rubin, D.B. (1987). Comment on “The Calculation of Posterior Distribution by Data Augmentation”, Journal of the American Statistical Association, 82, 543–546.

    Google Scholar 

  • Tanner, M.A. and Wong, W.H. (1987). “The Calculation of Posterior Distributions by Data Augmentation”, (with discussion), Journal of the American Statistical Association, 82, 528–550.

    MathSciNet  MATH  Google Scholar 

  • Zeger, S. and Karim, R. (1990). “Generalized Linear Models with Random Effects”, Technical Report.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Tanner, M.A. (1991). The Gibbs Sampler. In: Tools for Statistical Inference. Lecture Notes in Statistics, vol 67. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-0510-1_6

Download citation

  • DOI: https://doi.org/10.1007/978-1-4684-0510-1_6

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-97525-2

  • Online ISBN: 978-1-4684-0510-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics