Article,
Beta Processes, Stick-Breaking and Power Laws
Bayesian Anal., 7 (2): 439--476 (June 2012)
DOI: 10.1214/12-ba715
Abstract
The beta-Bernoulli process provides a Bayesian nonparametric prior
for models involving collections of binary-valued features. A draw from the beta
process yields an infinite collection of probabilities in the unit interval, and a
draw from the Bernoulli process turns these into binary-valued features. Recent
work has provided stick-breaking representations for the beta process analogous
to the well-known stick-breaking representation for the Dirichlet process. We de-
rive one such stick-breaking representation directly from the characterization of
the beta process as a completely random measure. This approach motivates a
three-parameter generalization of the beta process, and we study the power laws
that can be obtained from this generalized beta process. We present a posterior
inference algorithm for the beta-Bernoulli process that exploits the stick-breaking
representa
