The Dirichlet Distribution: A Density on the Simplex

Chapter 13 · Mathematics for AI and Machine Learning · Advanced · 1:42

An interactive live film: the Dirichlet density as a 3D surface over the triangle of probability vectors, flat at alpha = 1, a dome above one, climbing to the corners below one; the green line stands on the mean. Set alpha to hit a target mean and variance.

Narration

A probability vector over three categories is a point of this triangle on the floor: its coordinates are nonnegative and sum to one. This is the simplex.

The Dirichlet distribution puts a density on the triangle: a constant made of Gamma functions, times each coordinate raised to its concentration minus one. The height of the surface is that density.

The rest of the narration is in the book's Companion.