# beta process

(45 minutes to learn)

## Summary

The beta process is a random discrete measure that is completely described by a countably infinite set of atoms, where each atom has a finite mass determined from a stick-breaking process. Unlike the Dirichlet process, the weights of the atoms do not have to sum to one, but the masses must be between [0,1], and the marginals of the beta process are not beta distributed. The beta process can be used as a base measure for a Bernoulli process, i.e. to yield a stochastic process for binary random variables.

## Context

This concept has the prerequisites:

- Dirichlet process (The Dirichlet process is a useful analogy for understanding the beta process.)
- Indian buffet process (The IBP is the sequential process for sampling from a Bernoulli process with a beta process base-measure.)

## Core resources (read/watch one of the following)

## -Free-

→ Levy Processes and Applications to Machine Learning (2008)

## Supplemental resources (the following are optional, but you may find them useful)

## -Free-

→ Hierarchical Models, Nested Models and Completely Random Measures (2010)

→ Nonparametric Bayesian Models (2009)

## See also

- The IBP is often used in probabilistic models with binary latent features .