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Introduction

Unit 1

1. About This Course
2. Topics Covered
3. Software
4. A Simple Regression*

Unit 2

1. History of Bayesian Statistics
2. Historic Overview Links
3. Bayesian vs. Frequentist
4. Ten Coin Flips*
5. FDA Recommendations

Unit 3

1. A Review of Necessary Probability
2. Conditioning, Part 1
3. Conditioning, Part 2
4. Bayes’ Theorem
5. Manufacturing Bayes*
6. Two-headed Coin*
7. Bayes Networks
8. Alarm*
More Examples
- Supplementary Problem: Emily’s Vacation*
- Supplementary Exercises*

Unit 4

Probability Distributions
Bayes’ Theorem
Bayesian Inference in Conjugate Cases
Priors
Empirical Bayes
- 18. Parametric
- 19. Non-parametric
More Examples

Unit 5

Bayesian Computation
The Metropolis Algorithm
Gibbs Sampling
Other Algorithms
- 16. Hamiltonian Monte Carlo
- 17. Going Further
Supplementary Exercises

Unit 6

1. Probabilistic Programming Languages
2. A Gentle Introduction to DAGs for Bayesian Models
3. Joint Probability Graphs
4. More about PyMC
5. Loading Data, Step Function, and Deterministic Variables*
6. Missing Data*
7. Hypothesis Testing*
8. Prediction*
9. Type-1 Censoring*
10. The Zero Trick and Custom Likelihoods*

Unit 7

Hierarchical Models
Linear Models
Other Models
Supplementary Exercises

Unit 8

1. Missing Data
2. Rats Example with Missing Data*
3. Time-to-event Models
4. Time-to-event Models: Example 1
5. Time-to-event Models: Example 2*
6. Time-to-event Models: Gastric Cancer*
Supplementary Exercises

Unit 9

1. Model Fit, Selection, and Diagnostics
2. Deviance Information Criterion
3. Model Fit and Selection
4. Hald*
5. Conditional Predictive Ordinate
6. Gesell*
7. Using the Empirical CDF and the Probability Integral Transform
8. Cumulative Example*
9. Stochastic Search Variable Selection
10. SSVS: Hald*
Supplementary Exercises

Unit 10

1. Lister*
2. Dental Development*
3. Revisiting UK Coal Mining Disasters*
4. Rasch*
5. Wine Classification*
6. Predicting Using Censored Data*
7. Prediction of Time Series*

Appendix A

BUGS Examples, Volume 1
- 10 - Blocker
BUGS Examples, Volume 2
- 01 - Dugongs

Back Matter

1. Bibliography
2. Latex Reference

Repository
Open issue

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Bayesian Inference in Conjugate Cases

Bayesian Inference in Conjugate Cases#

9. Estimation
10. Credible Intervals
11. Gamma Gamma*
12. Bayesian Testing
13. Prediction

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8. Poisson–Gamma Model

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9. Estimation

By Georgia Tech ISYE 6420 Staff

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