Lecture 9: Gibbs Sampling and Data Augmentation

Readings

  • A First Course in Bayesian Statistical Methods by Peter D. Hoff
    • Chapter 6: Posterior approximation with the Gibbs sampler
    • Section 9.1: The linear regression model (review)
    • Section 9.2: Bayesian estimation for a regression model
    • Section 10.4: Metropolis, Metropolis-Hastings and Gibbs
    • Section 10.5: Combining the Metropolis and Gibbs algorithm
    • Section 10.6: Discussion and further references
    • Section 12.1 Latent Variables for Ordinal Data
  • Bayesian Data Analysis (Third Edition) by Andrew Gelman, John Carlin, Hal Stern, David Dunson, Aki Vehtari, and Donald Rubin
    • Section 11.1: Gibbs sampler
    • Section 11.2: Metropolis and Metropolis-Hastings algorithms
    • Section 11.3: Using Gibbs and Metropolis as building blocks
    • Section 11.7: Bibliographic note
    • Section 14.1: Conditional modeling
    • Section 14.2: Bayesian analysis of the classical regression model
  • Albert & Chib Bayesian Analysis of Binary and Polychotomous Response Data, Journal of the American Statistical Association, Vol. 88, No. 422 pp. 669- 679 )
  • The Bayesian Choice (Second Edition) by Christian Robert