This free course is an introduction to Bayesian statistics. Section 1 discusses several ways of estimating probabilities. Section 2 reviews ideas of conditional probabilities and introduces Bayes’ theorem and its use in updating beliefs about a proposition, when data are observed, or information becomes available. Section 3 introduces the main ideas of the Bayesian inference process. The prior distribution summarises beliefs about the value of a parameter before data are observed. The likelihood function summarises information about a parameter contained in observed data and the posterior distribution represents what is known about a parameter after the data have been observed.
Course learning outcomes
After studying this course, you should be able to:
use relative frequencies to estimate probabilities
calculate conditional probabilities
calculate posterior probabilities using Bayes' theorem
calculate simple likelihood functions
describe the role of the posterior distribution, the likelihood function and the posterior distribution in Bayesian inference about a parameter Ɵ.