Bayesian Statistics

Read these first

1. 01Credible Intervals and Posterior Summaries

   How to boil down a full Bayesian posterior distribution into the numbers people actually want to see, and why a Bayesian interval means exactly what most people mistakenly think a frequentist confidence interval means.

2. 02Gibbs Sampling

   A way to draw samples from a complicated joint posterior distribution you cannot write down directly, by repeatedly sampling one variable at a time from its conditional distribution while holding everything else fixed.

3. 03Hierarchical Bayesian Models

   How to estimate many related quantities at once, one win rate per trader, one beta per sector, so that groups with little data automatically borrow strength from the whole population instead of producing wild, unstable estimates on their own.

4. 04Variational Inference

   A way to approximate a hard Bayesian posterior almost instantly by finding the simplest, easy-to-describe distribution that's closest to it, trading exactness for speed when a full MCMC run is too slow to be useful.

Then the rest

1. 05Bayesian Versus Frequentist Interpretation
2. 06Bayesian Linear Regression
3. 07Posterior Predictive Checks
4. 08Prior Elicitation and Prior Choice
5. 09The Posterior Predictive Distribution
6. 10Bayes Factors
7. 11Bayesian Model Averaging
8. 12Empirical Bayes
9. 13Hamiltonian Monte Carlo and NUTS
10. 14Jeffreys and Noninformative Priors
11. 15Marginal Likelihood and Model Evidence
12. 16MCMC Convergence Diagnostics
13. 17Spike-and-Slab Priors
14. 18The Laplace Approximation
15. 19Thompson Sampling and Bayesian Bandits