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## For today you should have:

2. Prepared for a quiz.

## Today:

1. Quiz.
2. Project report "suggestions"
3. Bayesian Estimation exercise.
4. Coin problem.

1. Homework 8.

### Bayesian estimation

`We will start with an in-class exercise where we estimate the probability of heads, p, based on evidence.`
`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`
``confidence *= p``
`and if we get tails, the update is`
``confidence *= 1-p``
After each flip we can look at the location and shape of the distribution.
`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."`
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