WORKSHOP
IN STATISTICAL MIXTURES AND LATENT-STRUCTURE MODELLING
International Centre
for Mathematical Sciences, Edinburgh, March 28 - March 30,
2000
Radford Neal, Department
of Statistics University of Toronto
`Hierarchical mixtures using diffusion tree priors'
I introduce a family of prior
distributions over univariate or multivariate distributions, based on the
use of a "Dirichlet diffusion tree" to generate exchangeable data sets.
These priors can be viewed as generalizations of Dirichlet processes and
of Dirichletprocess mixtures. They are potentially of general use
for modeling unknown distributions, either of observed data or of latent
values. Unlike simple mixture models, Dirichlet diffusion tree priors can
capture the hierarchical structure that is present in many distributions.
Depending on the "divergence function" employed, a Dirichlet diffusion
tree prior can produce discrete or continuous distributions. Empirical
evidence is presented that some divergence functions produce distributions
that are absolutely continuous, while others produce distributions that
are continuous but not absolutely continuous. Although Dirichlet
diffusion trees are defined in terms of a continuous-time stochastic process,
inference for finite datasets can be expressed in terms of finite-dimensional
quantities, which should allow computations to be performed by reasonably
efficient Markov chain Monte Carlo methods. There is also a tech
report on this available from my web page, called
