AMS206B, Winter 2014, Section 01: Syllabus


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 modeldiagnostics, model selection and sensitivity analysis.


AMS-203. Enrollment restricted to graduate students.


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.


01/07 Introduction.

01/09 Review of distributions. Exponential families. Conjugate analysis.

01/14 Conjugate analysis.

01/16 Foundations: A decision theoretic approach to statistical inference.

01/21 Foundations: Priors and the subjective interpretation of probability. Exchangeability.

01/23 Bayesian point and interval estimation. Loss functions. Admissibility of

        Bayes estimators. Shrikage Priors. Bias and MSE of Bayes estimators.

01/28 More foundational issues. The likelihood principle. Sufficiency.

         Exchangeability revisited. Sequential updating.

01/30 More general priors and asymptotic properties of Bayesian estimates. Discrete case.

         Continuous case: Laplace expansions & “Bayesian CLT”. Approx inference.

02/04 More general priors: Simulation-based inference. MC integration. Generating pseudo-random variables (inversion, transformation, rejection).

02/06 More on random variate generation.

02/11 EXAM 1

02/13 Simulation-based inference: Importance sampling, Metropolis Hastings.

02/18 Simulation-based inference: Gibbs sampling.

02/20 Objective Bayes and estimation problems.

02/25 Bayesian hypothesis testing and model comparison.

02/27 Simulation-based methods for model comparison.

03/04 Objective Bayes and hypothesis testing.

03/06 EXAM 2

03/11 Hierarchical modeling and mixture representations. Data augmentation.

03/13 Complementary topics.


  • Robert, C. (2007) The Bayesian Choice. Second Edition, Springer Verlag: New York. Available electronically, UCSC library 
  • Hoff, P. (2009) A First Course in Bayesian Statistical Methods. Springer: New York. Available electronically, UCSC library. 
  • Berger J.O. (1984) Statistical Decision Theory and Bayesian Analysis. Springer. 
  • Bernardo, J.M. and Smith, A.F.M. (2000)  Bayesian Theory.

Gelman, A., Carlin, J.B., Stern, H.S., and Rubin, D.B. (2003). Bayesian Data Analysis. Second Edition. Chapman & Hall. 


Homework. There will be about 3-5 homework assignments. Some (typically 1-2 problems) of each homework will be graded. In addition, the exams will be based on the homework assignments so it is very important that you solve all the problems in each assignment. 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 also have to prepare a latex file (and resulting pdf file) with the solution. The file will be made available to the rest of the students through the class website. A template will be provided by the instructor.

Exams. There will be 2 exams.

Your Grade. Your course grade will be based on the exams and homework assignments as follows: (a) Homework 30%; (b) Presentation 5%; (c) Exam 1 30% and Exam 2 35%.