# dirichlet distribution

## 1. intuition

- the dirichlet distribution generalizes the beta distribution for multiple variables
- just like the beta distribution is the conjugate prior for the bernoulli (single trial) and binomial (multi-trial) distribution, the dirichlet distribution is the conjugate prior for the categorical (single trial) and multinomial (multi-trial) distribution
- What is the pdf of dirichlet with \(k\) parameters saying? "For the given dirichlet parameters, what is the probability of \(p_1,...,p_k\), where \(\sum p_i = 1\)?"
- You can see how this can be used to model the prior on a \(k\) sided die