Bayesian Statistics

This lesson is designed to introduce the reader to the basic concepts of Bayesian statistics, using the medium of M&Ms.

It is based on the lesson template used in Data Carpentry and Software Carpentry workshops.

Prerequisites

While there is a short primer on probability theory in the beginning, it is useful for readers to have a familiarity with the concept of probabilities and the basic rules by which they operate (conditional independence, summation rule).

Chapters 9 and 10 of The Foundations of Data Science are a great read.

Schedule

	Setup	Download files required for the lesson
00:00	1. Introduction	Key question (FIXME)
00:00	2. Probabilities, Frequencies and More	What is the difference between a probability and a frequency?
00:00	3. Calculations with Probabilities	What are the basic operations one can do with probabilities?
00:00	4. Bayes' Theorem	What is Bayes’ theorem? Why do we care?
00:00	5. Probabilitiy Distributions	What is a probability density function? What is a cumulative distribution function?
00:00	6. Inferring the Fraction of Blue M&Ms, Part 1: Problem Set-Up	What statistical questions can we ask about M&Ms?
00:00	7. M&M Problem, Part II: The Likelihood	What is the likelihood for the fraction of blue M&Ms?
00:00	8. Statistics with M&Ms, Part III: Setting good priors	How can we design an informative prior for the M&Ms problem?
00:00	9. Statistics with M&Ms, Part IV: Estimating the Posterior	Given a prior and a likelihood, can we calculate the posterior probability?
00:00	10. Bayesian Statistics in Astronomy: A Short Example	Key question (FIXME)
00:00	11. Advanced: A Hierarchical Model for M&Ms	Key question (FIXME)
00:00	12. Data Analysis in the Wild: Statistics and Ethics	How can we design statistical and data analysis procedures that are ethical?
00:00	Finish

The actual schedule may vary slightly depending on the topics and exercises chosen by the instructor.