(55 minutes to learn)
The beta distribution is a probability distribution over the unit interval. It is most commonly used in Bayesian statistics as the conjugate prior for the Bernoulli distribution.
This concept has the prerequisites:
- random variables
- expectation and variance
- gamma function (The gamma function is part of the normalizing constant of the beta distribution.)
- Know the PDF of the beta distribution
- Be able to compute the expectation of a beta random variable
- Express the uniform distribution as a special case of the beta distribution
Core resources (read/watch one of the following)
→ Probability and Statistics
An introductory textbook on probability theory and statistics.
Location: Section 5.10, "The beta distribution," pages 303-308
- binomial distribution
- The proof of the identity about products of gamma functions is optional.
Supplemental resources (the following are optional, but you may find them useful)
→ A First Course in Probability
An introductory probability textbook.
Location: Section 5.6.4, "The beta distribution," pages 240-241
- The beta distribution is the conjugate prior for the Bernoulli and binomial distributions.
- The Dirichlet distribution is a multivariate generalization of the beta distribution.
- create concept: shift + click on graph
- change concept title: shift + click on existing concept
- link together concepts: shift + click drag from one concept to another
- remove concept from graph: click on concept then press delete/backspace
- add associated content to concept: click the small circle that appears on the node when hovering over it
- other actions: use the icons in the upper right corner to optimize the graph placement, preview the graph, or download a json representation