## For today you should have:- Read Chapter 8
- Prepared for a quiz.
## Today:- Quiz.
- Project report "suggestions"
- Bayesian Estimation exercise.
- Coin problem.
- Homework 8.
- Read Chapter 9.
- Read this post about multiple regression.
## Bayesian estimation
The prior is a uniform distribution, or actually a discrete approximation of a uniform distribution. Each person in the room gets a difference value of p and a degree of confidence. If we get heads, each person updates with
and if we get tails, the update is
`With a large number of flips, the distribution converges on the actual value of p.` `Some lessons:` `1) It's ok to start with an unnormalized prior, but we do need the hypotheses to be ME and CE (mutually exclusive and collectively exhaustive).` `2) You can normalize the posterior after each flip, or leave it until the end. Same answer either way.` `3) The results depend on the prior, so in that sense it is subjective. But we can often use context to make justified decisions about the prior.` `4) With enough data, people with different priors converge, unless the priors are "immune to data."` |

Lecture notes >