High-level picture
“Bayesian Recipe”: high-level picture
- Construct a probability model including
- random variables for what we will measure/observe
- random variables for the unknown quantities
- those we are interested in (“parameters”, “predictions”)
- others that just help us formulate the problem (“nuisance”, “random effects”).
- Compute the posterior distribution (condition on the data)
- Use the posterior distribution to (decision theory):
- make prediction (point estimate)
- estimate uncertainty (credible intervals)
- make a decision
Plan
- First week: probability essentials (foundations for steps 1 and 2 of the Bayesian Recipe)
- Second week: steps 1, 2, 3 for one specific discrete probability models
- Third week and beyond: step 1, 2, 3 for arbitrary models
First step of the Recipe: “constructing a probability model”
- What is a model?
- What is a probability model?
- Example (week 2): building a probability model for the rocket launch problem.
What is a model?
(Scientific) model: A simplification of reality amenable to mathematical investigation.
\[\text{Reality} \xrightarrow{\text{Art + Scientific method}} \text{Model} \xrightarrow{\text{Mathematics}} \text{Prediction}\]
- In this course “mathematics” will be Bayesian analysis/probability theory.
- Bayesian analysis/probability theory assume a model as starting point.
- To create a first model is a bit of an art. It comes with data analysis experience.
- Then after we start with an initial model we can improve it by checking predictions against reality.