
Stats 270/370
A Course in Bayesian Statistics
This class is the first of a twoquarter 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.
 Introduction to Bayesian Statistics. Examples of current application of the Bayesian inferential framework. The fundamentals: prior, likelihood, posterior.
 Good (1983) 46656 Varieties
of Bayesians (#765) in Good Thinking.
The Foundations of Probability and Its Applications, Univeristy of Minnesota Peress, Minneapolis.
 Diaconis and Ylvisaker (1983) Quantifying Prior Opinion, Bayesian Statistics 2. Proc. 2nd Valencia Int'l Meeting, 983. J. M. Bernardo, M. H. Degroot, D. V. Lindley, A. F. M. Smith (eds.) NorthHolland, Amsterdam 133156 (1985).
 Lawrence CE, Altschul SF, Boguski MS, Liu JS, Neuwald AF, Wootton JC. (1993) Detecting subtle sequence signals: a Gibbs sampling strategy for multiple alignment, Science 262:20814.
 Liu, Neuwald and Lawrence (1995) Bayesian Models for Multiple Local Sequence Alignment and Gibbs Sampling Strategies JASA 90: 11651170.
 Bayes (1763) An essay toward solving a problem in the doctrine of chances, reprinted in 1958,
Biometrika 45:296315.
 Stigler (1982) Thomas Bayes's Bayesian Inference Journal of the Royal Statistical Society. Series A, 145:250258.
 Zabell, Sandy W. E. Johnson's "Sufficientness" Postulate, Ann. Statist. 10 (1982), no. 4, 10901099.

Diaconis and Holmes (2002) A Bayesian peak into Feller volume I Sankhya Series A 3:820841.
 Deeper understanding of Bayesian calculus
 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.
 Exponential families and conjugate priors
 Gaussian
 Choices of prior distributions. Invariance, non informative priors.
 Subjective definition of probability. Coherence, betting schemes.
 Exchangeability
 Inferential principles Sufficiency, likelihood principle, ancillarity
 Bayesian regression Standard framework for multivariate gaussian distributios; prior distribution on variancecovariance matrix; multivariate regression methods.
 Computation How to explore the posterior: numerical integration, importance sampling, MCMC schemes.
 Hierarchical models and computation . Examples of MCMC; empirical bayes; applications.
Grading will be based on problem set and final project.
Problemsets 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, 3:155:15pm in 420371 (Jordan Hall).
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