Exercise

# Bayesian updating

Suppose Rebekah is using a beta density with shape parameters 8.13 and 3.67 to reflect her current knowledge about `P`

(the proportion of college women who think they are overweight). In a sample survey, 16 out of 20 students surveyed think they are overweight.

Here our definition of a "success" is thinking one is overweight, so we observe 16 successes and 4 failures.

The posterior density for `P`

will make a beta curve with new parameters \(8.13 + 16 = 24.13\) and \(3.67 + 4 = 7.67\). The graph on the right displays the prior (blue) and posterior (red) curves.

Instructions

**100 XP**

Harry has a different prior for `P`

. His beliefs are represented by a beta curve with parameters 3 and 3. His best guess at `P`

is 0.5 and he is relatively unsure about this guess.

- Define a vector
`ab`

containing the shape parameters for Harry's prior. - Define a vector
`sf`

containing the observed successes and failures. - Compute the vector
`ab_new`

of shape parameters for Harry's beta posterior. - Use the function
`beta_draw()`

to draw Harry's posterior beta curve.