One specific prior discussed in the previous lecture is the Beta distribution, which was then demonstrated in a scenario with a Bernoulli statistical model. Which of the follwing statements is/are true about the Beta distribution, written as \textsf{Beta}(\alpha , \beta ) \propto p^{\alpha -1}(1-p)^{\beta -1}?
The Beta distribution is very suited to models where our parameter represents a probability due to its support being [0, 1].
The Beta distribution is very suited to models where our parameter represents a probability due to its maximum always being close to \frac{1}{2}.
The Beta distribution is very suited to models where our parameter represents a probability because multiplying it by p or 1-p simply involves incrementing the respective parameter.
All three statements are true about the Beta distribution.
The true statement about the Beta distribution is:
- The Beta distribution is very suited to models where our parameter represents a probability due to its support being [0, 1].
Explanation: The Beta distribution is commonly used as a prior distribution for modeling probabilities because its support is in the range [0, 1], which is the range of probabilities.