Lecture 18: Outliers and Robust Bayesian Regression

Readings

• Hamura, Y.. (2023) A Simple Proof of Posterior Robustness

• Desgagné, A. and Gagnon P (2018) Bayesian Robustness to Outliers in Linear Regression and Ratio Estimation

• West, M. (1984). Outlier Models and Prior Distributions in Bayesian Linear Regression. JRSS B 46, 431-439

• Hoeting, J., Raftery, A., Madigan, D. (1996) A method for simultaneous variable selection and outlier identification in linear regression Computational Statistics & Data Analysis, 22, 251-270

-O’hagan, T. (1979) On Outlier Rejection Phenomena in Bayes Inference. JRSSB, 41:358-367

• A First Course in Bayesian Statistical Methods by Peter D. Hoff

  • Section 9.1: The linear regression model (review)
  • Section 9.2: Bayesian estimation for a regression model
  • Section 9.3: Model Selection (linear regression)

• Bayesian Data Analysis (Third Edition) by Andrew Gelman, John Carlin, Hal Stern, David Dunson, Aki Vehtari, and Donald Rubin

  • Section 14.2: Bayesian analysis of the classical regression model

• The Bayesian Choice (Second Edition) by Christian Robert