# Dirichlet Distribution The **Dirichlet Distribution** provides a[ distribution over a *vector* of probabilities](https://youtu.be/CEVELIz4WXM?t=433). For instance, imagine you are a customs agent stamping incoming passports. Each person will have a passport associated with a specific country. Assume for now that there are only 20 countries. Then, we can model the probability of observing each country with a specific parameter, $p_i$, where $i$ is the index of the current country. We will end up with a vector of length $20$, with the constraint that it's entries must sum to 1. Note that this is a generalization of the [Beta Distribution](Beta%20Distribution.md). This is very important to keep in mind when trying to estimate *multiple probabilities* because probabilities are correlated! Knowing one provides you information about the others. ### Geometric Intuition The following intuition is useful: The dirichlet distribution can be thought of as a triangle (**simplex**) over a space. ### Visual  ### Analogy Beta is to the Binomial Distribution as the Dirichlet is to the Multinomial Distribution. --- Date: 20220510 Links to: Tags: #review References: * [Continuous Distributions: Beta and Dirichlet Distributions - YouTube](https://www.youtube.com/watch?v=CEVELIz4WXM) * Bayesian Methods for Hackers, chapter 7, pg 199 ### Anki START Basic What distribution should be used when trying to model a *vector* of probabilities? Back: Dirichlet Distribution Tags: math <!--ID: 1652213501446--> END