Resources and Handouts

Course Information

Notes on maximum likelihood estimation for GLMs

 

References on Bayesian approaches to modeling and inference with GLMs

BOOKS

  • Johnson, V.E. and Albert, J.H. (1999). Ordinal Data Modeling. Springer.
  • D. Dey, S.K. Ghosh, B.K. Mallick (editors) (2000). Generalized Linear Models: A Bayesian Perspective (Number 5 in the series: "Biostatistics: A Series of References and Textbooks"). Marcel Dekker.
  • Gelman, A., Carlin, J.B., Stern, H.S. Dunson, D.B., Vehtari, A. and Rubin, D.B. (2014). Bayesian Data Analysis (Third Edition). CRC, Chapman and Hall.

 

PAPERS

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.

 

MCMC methods for posterior simulation

  • 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.

 

Methods for 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.

 

Extensions of the GLM setting

  • Albert, J.H. (1988). Computational methods using a Bayesian hierarchical generalized linear model. Journal of the American Statistical Association, 83, 1037-1044.
  • Gelfand, A.E., Sahu, S.K. and Carlin, B.P. (1996). Efficient parameterizations for generalized linear mixed models. In Bayesian Statistics 5, eds. J.M. Bernardo, J.O. Berger, A.P. Dawid, and A.F.M. Smith. Oxford University Press, pp. 165-180.
  • Dey, D.K., Gelfand, A.E. and Peng, F. (1997). Overdispersed generalized linear models. Journal of Statistical Planning and Inference, 64, 93-107.
  • Diggle, P.J., Tawn, J.A. and Moyeed, R.A. (1998). Model-based geostatistics (with discussion). Applied Statistics, 47, 299-350.
  • Hsu, J.S.J. and Leonard, T. (1997). Hierarchical Bayesian semiparametric procedures for logistic regression. Biometrika, 84, 85-93.
  • Neal, R.M. (1997). Monte Carlo implementation of Gaussian process models for Bayesian regression and classification. Technical Report No. 9702, Dept. of Statistics, University of Toronto.
  • Kleinman, K.P. and Ibrahim, J.G. (1998). A Semi-parametric Bayesian approach to generalized linear mixed models. Statistics in Medicine, 17, 2579-2596.
  • Chib, S. and Carlin, B.P. (1999). On MCMC sampling in hierarchical longitudinal models. Statistics and Computing, 9, 17-26.
  • Brooks, S.P. (2001). On Bayesian analyses and finite mixtures for proportions. Statistics and Computing, 11, 179-190.
  • Ibrahim, J.G., Chen, M.-H. and Lipsitz, S.R. (2002). Bayesian methods for generalized linear models with covariates missing at random. The Canadian Journal of Statistics, 30, 55-78.
  • DeYoreo, M. and Kottas, A. (2016). Bayesian nonparametric modeling for multivariate ordinal regression.