Unit 10 of 12
Bayesian Statistics
- 3 lessons
- Videos 71 to 73
Bayesian statistics describes uncertainty about unknown quantities with probabilities and updates them with data. This unit covers priors, posteriors, credible intervals and prediction.
The posterior is proportional to the prior times the likelihood, first for a few competing hypotheses and then for a success probability with a beta prior. A 95% credible interval contains the parameter with posterior probability 95% given the prior, the model and the data, which is a different statement from a 95% confidence level. Posterior predictive distributions describe future observations. Refitting with other reasonable priors shows how much a conclusion depends on the prior, and predictive checks look for patterns in the data that the model fails to reproduce.
Every lesson will be one video. The videos are coming soon, and each lesson page already has the definitions and an example for every key term.
Bayesian Inference
Prior, Likelihood and Posterior
How Bayesian updating turns a prior distribution over competing hypotheses into a posterior distribution, what the normalizing constant does, and how prior odds, posterior odds and the Bayes factor fit together.
Video 71
Bayesian Estimation and Credible Intervals
How a beta prior and a binomial likelihood give a beta posterior for a success probability, how the posterior mean and median summarize it, and what an equal-tailed credible interval says and does not say.
Video 72
Posterior Prediction and Prior Sensitivity
How the posterior predictive distribution forecasts new outcomes by averaging over parameter uncertainty, why outcomes sharing one unknown probability are dependent, and how prior sensitivity and predictive checks probe a model.
Video 73