# The Bayesian recipe

## Outline

### Topics

- Introduce the Bayesian Recipe (synonym for the Bayes estimator)
- Illustrate it using this week’s running example

### Rationale

The Bayesian Recipe/Bayes estimator is the guide for all “full Bayesian” statistical analyses. This week we apply it to an example that builds on last week’s review.

## This week’s running example

- You are consulting for a satellite operator
- They are about to send a $100M satellite on a Delta 7925H rocket

**Data**: as of Jan 2024, Delta 7925H rockets have been launched 3 times, with 0 failed launches- Note: Delta 7925H is not reusable, so each rocket is “copy- built” from the same blueprint

- Should you recommend buying a $2M insurance policy?

**Convention:** use 1 for a success, 0 for a failure.

## The Bayesian recipe

The goal this week is to undersand the 3 steps in the Bayesian recipe:

- 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

- Understanding Step 1 (“construct a probability model”):
- we reviewed probability models last week,
- in fact, the model we use for this week’s problem is the same as last week’s!
- We will just need to add some Bayesian terminology:
**prior, likelihood**.

- Understanding Step 2 (“condition on the data”):
- we reviewed conditional probability last week,
- in fact, the conditional probability calculation for this week’s problem is the same as last week’s!
- We just need to add some Bayesian terminology:
**posterior distributions**.

- Understanding Step 3: this is where most of the new material will be for this week.