UNIT 1

• 1.1 About the Class. Discussion od Syllabus. Expectations and Deliverables
• 1.2 Software WinBUGS/OpenBUGS. Installation. WinBUGS on MACs.
• 1.3 Software MATLAB/Octave.
• 1.4 Examples.

UNIT 2

• 2.1 Historic Overview. The Reverend Thomas Bayes. The Essay
• 2.2 Bayesian vs. Classical Statistics. Models and Parameters. 10 coin flips.
• 2.3 FDA Recommendations

UNIT 3

• 3.1 A Review of Necessary Probability. Events and Probabilities. Example: Circuit Problem
• 3.2 Conditioning
  • Independence, Conditional Probability
  • Hypotheses, Total Probability
  • Examples: Queen of Spades, Manufacturing Bayes, and Bridged Circuit
• 3.3 Bayes Formula
  • From Prior to Posterior
  • Bayesian Learning
  • Examples: Manufacturing Bayes Continued, Bridged Circuit, Two-headed Coin
• 3.4 Basic Bayes Networks
  • More on WinBUGS
  • DAG, Propagation of Evidence
  • Example: Alarm
• 3.5 Exercises for Unit 3
• 3.6 Homework 1

UNIT 4

• 4.1 Basic Distributions
  • Models and Parameters
  • Numerical Characteristics
  • Joint and Conditional Distributions
  • Worked Examples: Discrete and Continuous
• 4.2 Bayes Theorem
  • Ingredients for Bayesian Inference
  • Conjugate Families
  • Examples: Jeremy's IQ, 10 flips of Coin, and Poisson--Gamma Pair
• 4.3 Exercises for Unit 4 (Part 1);
• 4.4 Homework 2
• 4.5 Bayesian Inference in Conjugate Cases
  • Bayesian Estimation
  • Credible Sets
  • Bayesian Testing
  • Bayesian Prediction
  • Examples: Jeremy's IQ, 10 flips of Coin
  • Jeremy and flips in WinBUGS
• 4.6 Prior Elicitation
  • Elicitation from Numerical Characteristics
  • Non-Informative Priors
  • ``Prior Sample Size.''
  • Example: eBay Purchase (WinBUGS)
• 4.7 Empirical Bayes
  • Parametric Approach
  • Non-Parametric Approach
• 4.8 Exercises for Unit 4 (Part 2)
• 4.9 Homework 3

UNIT 5

• 5.1 Bayesian Computation
  • Numerical Approaches
  • MCMC Methodology
• 5.2 Metropolis Algorithm
  • Theoretical Background
  • Example coded in Python, R, and Octave
• 5.3 Gibbs Sampling
  • Theoretical Background
  • Example coded in Python, R, and Octave
  • Beyond Gibbs and Metropolis
• 5.4 Exercises for Unit 5
• 5.5 Homework 4

MIDTERM EXAM

• MID.1 Review for Midterm
• MID.2 MIDTERM POSTED

UNIT 6

• 6.1 Graphical Models
  • More General DAGs.
  • Doodle BUGS
• 6.2 More About WinBUGS
  • Distributions and Data Input
  • Functions in WinBUGS
  • Examples Built In
  • Getting Help in WinBUGS
• 6.3 Advanced WinBUGS
• 6.4 Other Software for Bayesian Calculation
• 6.5 Exercises for Unit 6

UNIT 7

• 7.1 Hierarchical Models
  • Priors with Structural Information
  • Hidden Mixtures
  • Meta-Analysis
• 7.2 Bayesian Linear Models
  • Bayesian One- and Two-Way ANOVA. STZ and CR Constraints
  • Bayesian Multiple Regression
• 7.3 Other Models
  • Generalized Linear Models
  • Logistic, and Poisson Regressions
  • Multinomial Regression
  • Multilevel Models
• 7.4 Exercises for Unit 7
• 7.5 Homework 5

UNIT 8

• 8.1 Missing Data
  • Bayesian Handling of Missingness
  • Examples in WinBUGS
• 8.2 Censored Data
  • Time-to-Event Modeling
  • How to Censor in WinBUGS
  • Examples from Survival and Reliability Theory
• 8.3 Exercises for Unit 8

UNIT 9

• 9.1 Model Building and Selection
  • Variable Selection in Regression
  • Ibrahim--Laud Criterion
  • Examples in WinBUGS
• 9.2 Model Checking
  • Goodness-of-Fit
  • Deviance Information Criteria (DIC)
  • Posterior Predictive Checks
• 9.3 Exercises for Unit 9
• 9.4 Homework 6

UNIT 10

• 10.1 Applications and Case Studies
  • Meta Analysis
  • Next eruption of Vesuvius and Katla
  • Rash-type Models
  • Predicting in ARMA Model.
• 10.2 Project: My Own Bayesian Data Analysis (An Open-Ended Project)

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ISyE6420 by Brani Vidakovic is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.