Chapter 3 M3: Bayesian methods

In this module, we adopt a whole different philosophy about how certain things work: parameters, estimation, probability, truth, knowledge, etc. Although Bayesian statistics is a whole big field worthy of many, many courses, we’ll take a look at the foundational principles here and explore how Bayesian methods can be used for some specific problems.

Learning goals for this module include:

• Define the key types of distributions used in Bayesian modeling: the data model, prior model, posterior distribution, and posterior predictive distribution
  • This includes both describing/defining these objects in general (what do they mean? what do they tell you?), and identifying/writing them for a specific context or example.
• Use and describe the relationships between these distributions
  • Again, both describing them in the abstract and also working out specific examples – for example, writing out one distribution based on information you’re given about the others.
• Describe the use of Monte Carlo integration
  • On an activity or PP, you might need to actually do the whole process. On an Assessment, you’d need to talk about how the process works (including the math, yes!), how it’s used, and why it’s helpful.