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- Gibbs Sampling
Methods for
Stick Breaking
Priors: Journal of the
American
Statistical
Association
(March 2001),
pp. 161-173.A
rich and
flexible class
of random
probability
measures,
which we call
stick-breaking
priors, can be
constructed
using a
sequence of
independent
beta random
variables.
Examples of
random
measures that
have this
characterizati
on include the
Dirichlet
process, its
two-parameter
extension, the
two-parameter
Poisson–Dirich
let process,
finite
dimensional
Dirichlet
priors, and
beta
two-parameter
processes. The
rich nature of
stick-breaking
priors offers
Bayesians a
useful class
of priors for
nonparametric
problems,
while the
similar
construction
used in each
prior can be
exploited to
develop a
general
computational
procedure for
fitting them.
In this
article we
present two
general types
of Gibbs
samplers that
can be used to
fit posteriors
of Bayesian
hierarchical
models based
on
stick-breaking
priors. The
first type of
Gibbs sampler,
referred to as
a Pólya urn
Gibbs sampler,
is a
generalized
version of a
widely used
Gibbs sampling
method
currently
employed for
Dirichlet
process
computing.
This method
applies to
stick-breaking
priors with a
known Pólya
urn
characterizati
on, that is,
priors with an
explicit and
simple
prediction
rule. Our
second method,
the blocked
Gibbs sampler,
is based on an
entirely
different
approach that
works by
directly
sampling
values from
the posterior
of the random
measure. The
blocked Gibbs
sampler can be
viewed as a
more general
approach
because it
works without
requiring an
explicit
prediction
rule. We find
that the
blocked Gibbs
avoids some of
the
limitations
seen with the
Pólya urn
approach and
should be
simpler for
nonexperts to
use.
Source: Journal of the American Statistical Association (March 2001), pp. 161-173.
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