Syllabus and Class Information
COURSE DESCRIPTION
The course covers Bayesian statistical methods for inference and prediction including: estimation; model selection and prediction; exchangeability; prior, likelihood, posterior and predictive distributions; coherence and calibration; conjugate analysis; Markov Chain Monte Carlo methods for simulation-based computation; hierarchical modeling; Bayesian model diagnostics, model selection and sensitivity analysis.
PREREQUISITES
AMS-203. Enrollment restricted to graduate students.
LOCATION AND TIME
Thimann Lab 101 Tu-Th 10:00-11:45am
BIBLIOGRAPHY
The following is a list of books that will be used. You don’t need to buy any of them (some are available electronically from the UCSC library), but I recommend The Bayesian Choice by C. Robert if you want to buy just one. Additional reading material will be available online.
• Robert, C. (2007) The Bayesian Choice. Second Edition, Springer Verlag: New York. Available electronically through the UCSC library
• Berger, J.O. (1984) Statistical Decision Theory and Bayesian Analysis. Springer.
• Hoff, P. (2009) A First Course in Bayesian Statistical Method. Springer Verlag: New York. Available electronically through the UCSC library
• Gelman, A., Carlin, J.B., Stern, H.S., Dunson, D.B., Vehtari, A. and Rubin, D.B. Robert, C. (2007) Bayesian Data Analysis. Third Edition, Chapman & Hall.
EVALUATION
Homework. There will be about 3-5 homework assignments. The homework will not be graded but the exams will be based on the homework assignments so it is very important that you solve all the problems in each assignment. There will be homework presentations, i.e., during the last +/-30 minutes of some of the lectures groups of 1-2 students will be presenting the solutions to selected homework problems (the problems will be provided at least one week prior to the presentation). The students who present the solutions to a set of problems will also have to prepare a latex file (and resulting pdf file) with the solution. The file will be available to the rest of the students through the class website. A template will be provided by the instructor. The homework presentations will be graded.
Exams. There will be two exams and a final exam. All the exams will have an in class part and some may have a take home part (probably only the final).
Your Grade. Your course grade will be based on the exams and homework presentations as follows: (a) Exam 1: 25% (b) Exam 2: 25% (c) Final: 35% (d) Homework presentation: 15%.
CLASS SCHEDULE
Below is the tentative class schedule. Please check the online schedule as the list of topics and/or the dates when such topics will be covered may change.
DATE TOPICS
01/05 Introduction.
01/07 Review of distributions. Exponential Families. Conjugate Families.
01/12 Conjugate Analysis.
01/14 Foundations: A decision theoretic approach to statistical inference.
01/19 Bayesian point and interval estimation. Loss functions. Admissibility of Bayes estimators. Shrinkage priors. Bias and MSE of Bayes estimators.
01/21 Foundations: Exchangeability. Priors and the subjective interpretation of probability.
01/26 More foundational issues. The likelihood principle. Sufficiency. Exchangeability revisited. Sequential updating.
01/28 More general priors: Non-informative priors and reference priors.
02/02 Asymptotic properties of Bayesian estimates. Discrete case. Continuous case: Laplace expansions and Bayesian CLT. Approximate Inference.
02/04 EXAM 1
02/09 Simulation-based inference. Random generation.
02/11 Simulation-based inference: Importance sampling, Metropolis-Hastings.
02/16 Simulation-based inference: Gibbs sampling.
02/18 Objective Bayes and estimation problems.
02/23 Bayesian hypothesis testing and model comparison.
02/25 Simulation-based methods for model comparison.
03/01 Objective Bayes and hypothesis testing.
03/03 EXAM 2
03/08 Hierarchical models and mixture representations. Data augmentation.
03/10 Complementary topics.
03/14 12-3pm FINAL EXAM