Priors

Content for Tuesday, September 26, 2023

Content

  • Conjugate, flat, vague, Jeffrey’s, informative and penalized complexity priors
  • Priors for regression models
  • Parameter elicitation
  • Prior sensitivity analysis

Learning objectives

At the end of the chapter, students should be able to

  • choose a suitable prior for a Bayesian analysis
  • derive parameters of posterior distributions in conjugate models
  • perform parameter elicitation
  • assess the impact of priors through sensitivity analysis

Readings

Warning

These readings should be completed before class, to ensure timely understanding and let us discuss the concepts together through various examples and case studies — the strict minimum being the course notes.

Complementary readings

Warning

Complementary readings are additional sources of information that are not required readings, but may be useful substitutes. Sometimes, they go beyond the scope of what we cover and provide more details.

Slides

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References

Gelman, A. (2006). Prior distributions for variance parameters in hierarchical models (comment on article by Browne and Draper). Bayesian Analysis, 1(3), 515–534. https://doi.org/10.1214/06-BA117A
Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis (3rd ed.). Chapman; Hall/CRC. https://doi.org/10.1201/b16018
Johnson, A. A., Ott, M. Q., & Dogucu, M. (2022). Bayes rules! An introduction to applied Bayesian modeling (1st ed.). Chapman; Hall/CRC. https://doi.org/10.1201/9780429288340
Simpson, D., Rue, H., Riebler, A., Martins, T. G., & Sørbye, S. H. (2017). Penalising model component complexity: A principled, practical approach to constructing priors. Statistical Science, 32(1), 1–28. https://doi.org/10.1214/16-STS576
Villani, M. (2023). Bayesian learning: A gentle introduction. https://mattiasvillani.com/BayesianLearningBook/