
Bayesian Statistics for Beginners
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Content
- Section 1
- Basics of Probability
- 1: Introduction to Probability
- 2: Joint, Marginal, and Conditional Probability
- Section 2
- Bayes' Theorem and Bayesian Inference
- 3: Bayes' Theorem
- 4: Bayesian Inference
- 5: The Author Problem - Bayesian Inference with Two Hypotheses
- 6: The Birthday Problem: Bayesian Inference with Multiple Discrete Hypotheses
- 7: The Portrait Problem: Bayesian Inference with Joint Likelihood
- Section 3
- Probability Functions
- 8: Probability Mass Functions
- 9: Probability Density Functions
- Section 4
- Bayesian Conjugates
- 10: The White House Problem: The Beta-Binomial Conjugate
- 11: The Shark Attack Problem: The Gamma-Poisson Conjugate
- 12: The Maple Syrup Problem: The Normal-Normal Conjugate
- Section 5
- Markov Chain Monte Carlo
- 13: The Shark Attack Problem Revisited: MCMC with the Metropolis Algorithm
- 14: MCMC Diagnostic Approaches
- 15: The White House Problem Revisited: MCMC with the Metropolis-Hastings Algorithm
- 16: The Maple Syrup Problem Revisited: MCMC with Gibbs Sampling
- Section 6
- Applications
- 17: The Survivor Problem: Simple Linear Regression with MCMC
- 18: The Survivor Problem Continued: Introduction to Bayesian Model Selection
- 19: The Lorax Problem: Introduction to Bayesian Networks
- 20: The Once-ler Problem: Introduction to Decision Trees
- Appendices
- Appendix 1: The Beta-Binomial Conjugate Solution
- Appendix 2: The Gamma-Poisson Conjugate Solution
- Appendix 3: The Normal-Normal Conjugate Solution
- Appendix 4: Conjugate Solutions for Simple Linear Regression
- Appendix 5: The Standardization of Regression Data
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