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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
  • Colab
  • Repository
  • Open issue
  • .ipynb

Hierarchical Models

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*

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10. The Zero Trick and Custom Likelihoods*

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1. Introduction to Hierarchical Models

By Georgia Tech ISYE 6420 Staff

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