Bayesian Statistics for Beginners

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