Notes, handouts, resources

Course information

 Definitions and MLE estimation for GLMs (notes)

 

References on Bayesian modeling and inference for GLMs

Priors

  • West, M. (1985). Generalized linear models: Scale parameters, outlier accommodation and prior distributions. In Bayesian Statistics 2, eds. J. Bernardo, M.H. DeGroot, D.V. Lindley, and A.F.M. Smith. Amsterdam: North Holland, pp. 531-558.
  • Ibrahim, J.G. and Laud, P.W. (1991). On Bayesian analysis of generalized linear models using Jeffreys's prior. Journal of the American Statistical Association, 86, 981-986.
  • Bedrick, E.J., Christensen, R. and Johnson, W. (1996). A new perspective on priors for generalized linear models. Journal of the American Statistical Association, 91, 1450-1460.
  • Gelfand, A.E. and Sahu, S.K. (1999). Identifiability, improper priors, and Gibbs sampling for generalized linear models. Journal of the American Statistical Association, 94, 247-253.

Posterior simulation methods

  • Albert, J.H. and Chib, S. (1993). Bayesian analysis of binary and polychotomous response data. Journal of the American Statistical Association, 88, 669-679.
  • Dellaportas, P. and Smith, A.F.M. (1993). Bayesian inference for generalized linear and proportional hazards models via Gibbs sampling. Applied Statistics, 42, 443-459.
  • Gamerman, D. (1997). Sampling from the posterior distribution in generalized linear mixed models. Statistics and Computing, 7, 57-68.
  • Damien, P., Wakefield, J. and Walker, S. (1999). Gibbs sampling for Bayesian non-conjugate and hierarchical models by using auxiliary variables. Journal of the Royal Statistical Society, Series B, 61, 331-344. 
  • Holmes, C.C. and Held, L. (2006). Bayesian auxiliary variable models for binary and multinomial regression. Bayesian Analysis, 1, 145-168.
  • Polson, N.G., Scott, J.G. and Windle, J. (2013). Bayesian inference for logistic models using Polya-Gamma latent variables. Journal of the American Statistical Association, 108, 1339-1349.

Model assessment/model comparison

  • Albert, J.H. and Chib, S. (1995). Bayesian residual analysis for binary response regression models.  Biometrika, 82, 747-759. 
  • Raftery, A.E. (1996). Approximate Bayes factors and accounting for model uncertainty in generalised linear models. Biometrika, 83, 251-266. 
  • Gelfand, A.E. and Ghosh, S.K. (1998). Model choice: A minimum posterior predictive loss approach. Biometrika, 85, 1-11.
  • Goutis, C. and Robert, C.P. (1998). Model choice in generalised linear models: A Bayesian approach via Kullback-Leibler projections. Biometrika, 85, 29-37. 
  • Spiegelhalter, D.J., Best, N.G., Carlin, B.P. and van der Linde, A. (2002). Bayesian measures of model complexity and fit (with discussion). Journal of the Royal Statistical Society, Series B, 64, 583-639.
  • Chen, M.-H., Dey, D.K. and Ibrahim, J.G. (2004). Bayesian criterion based model assessment for categorical data. Biometrika, 91, 45-63.
  • McKinley, T.J., Morters, M. and Wood, J.L.N. (2015). Bayesian model choice in cumulative link ordinal regression models. Bayesian Analysis, 10, 1-30.