4.1 Introductory Example

• First, let’s remember:

• Three friends (feminist, clueless, optimist) discuss the proportion ($\pi$) of recent movies that pass the Bechdel test (representation of women in film).

• Which Beta prior corresponds to each of the friends?

• The three friends agree to review a sample of n recet movies and record Y, the number of movies that pass the Bechdel test.
• Y is the number of ‘successes’ in a fixed number of independent trials.

$$Y \sim {Bin}(n,\,\pi)$$ $$\pi \sim {Beta}(\alpha,\,\beta)$$

• Each analyst has their own unique posterior model of $\pi$.

$$\pi|(Y = y) \sim {Beta}(\alpha + y,\,\beta + n -y)$$