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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
1. Basic Distributions
2. Numerical Characteristics of Random Variables
3. Joint and Conditional Distributions
Bayes’ Theorem
4. Ingredients for Bayesian Inference
5. Conjugate Families
6. Example: Jeremy’s IQ
7. Ten Coin Flips Revisited: Beta Plots*
8. Poisson–Gamma Model
Bayesian Inference in Conjugate Cases
9. Estimation
10. Credible Intervals
11. Gamma Gamma*
12. Bayesian Testing
13. Prediction
Priors
14. Prior Elicitation
15. Non-informative Priors
16. Prior Sample Size
17. eBay Purchase Example*
Empirical Bayes
18. Parametric
19. Non-parametric
More Examples
Counts of Alpha Particles*
Supplementary Exercises 4.3
Supplementary Exercises 4.8
Unit 5
Bayesian Computation
1. Numerical Approaches
2. Normal–Cauchy Example
3. Laplace’s Method
4. Laplace’s Method Demo*
5. Markov Chain Monte Carlo
The Metropolis Algorithm
6. Metropolis
7. Metropolis: Normal-Cauchy*
8. Metropolis–Hastings: Weibull-Exponential Example
9. Weibull Lifetimes*
Gibbs Sampling
10. Introduction to Gibbs Sampling
11. Normal-Cauchy Gibbs Sampler*
12. Conjugate Gamma-Poisson Model
13. Pumps*
14. Change Point Problem
15. Coal Mining Disasters in the UK*
Other Algorithms
16. Hamiltonian Monte Carlo
17. Going Further
Supplementary Exercises
Unit 6
1. Probabilistic Programming Languages
2. Creating a Graphical Model
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
1. Introduction to Hierarchical Models
2. Reasons to Use Hierarchical Models
3. Priors with Structural Information
4. Priors as Hidden Mixtures*
5. Meta-analysis via Hierarchical Models*
Linear Models
6. Analysis of Variance
7. Coagulation*
8. Factorial Designs
9. Simvastatin*
10. Simple Linear Regression
11. Brozek index prediction*
12. Multiple Linear Regression
13. Multiple Regression: Brozek Index Prediction*
Other Models
14. Generalized Linear Models
15. GLM Examples*
16. Multinomial Logit
17. Multinomial regression*
18. Multilevel Models
19. Paraguay Vaccination Status*
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*
Back Matter
1. Bibliography
2. Latex Reference
Repository
Open issue
Index
