Stats 270/370

A Course in Bayesian Statistics

This class is the first of a two-quarter sequence that will serve as an introduction to the Bayesian approach to inference, its theoretical foundations and its application in diverse areas. The instructors are Persi Diaconis, Chiara Sabatti and Wing Wong. Following is a tentative outline of lectures. As we move through the quarter, it will become more precise and reflect, week by week, the material actually covered in class.

  1. Introduction to Bayesian Statistics. Examples of current application of the Bayesian inferential framework. The fundamentals: prior, likelihood, posterior.
  2. Deeper understanding of Bayesian calculus
    1. Bayes theorem for the non dominated case.
      • "Probability and potentials", by Paul A. Meyer. Blaisdell, New York, 1966
      • Look for 'Regular conditional probability' in "Probability" by Breiman, "Probability and measure", Billingsley.
    2. Exponential families and conjugate priors
    3. Gaussian
  3. Choices of prior distributions. Invariance, non informative priors.
  4. Subjective definition of probability. Coherence, betting schemes.
  5. Exchangeability
  6. Inferential principles Sufficiency, likelihood principle, ancillarity
  7. Bayesian regression Standard framework for multivariate gaussian distributios; prior distribution on variance-covariance matrix; multivariate regression methods.
  8. Computation How to explore the posterior: numerical integration, importance sampling, MCMC schemes.
  9. Hierarchical models and computation . Examples of MCMC; empirical bayes; applications.
  • Graphical models

Grading will be based on problem set and final project. Problem-sets will be assigned weekly and due the following week on wednesday. By the end of week 5 each student should have handed in a proposal for a final project. A list of possible topics will be distributed by the instructors during the first weeks of classes. The completed final projects are going to be due Friday March 18, which is the scheduled date for the exam for this class. There will be no exam other then the final project.

The TAs for the class are Joey Arthur and Weijie Su. Office hours for the month of January are Monday and Thursday, 3:15-5:15pm in 420-371 (Jordan Hall).

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