Statistical Research Report
Preprint 7, 2000
Author(s):
N.L. Hjort
Title:
Bayesian analysis for a generalised Dirichlet process
prior.
Abstract:
A family of random probabilities is defined and studied.
This family contains the Dirichlet process as a special case,
corresponding to an inner point in the appropriate parameter space.
The extension makes it possible to have random means with
larger or smaller skewnesses as compared to skewnesses
under the Dirichlet prior, and also in other ways amounts to
additional modelling flexibility.
The usefulness of such random probabilities for
use in nonparametric Bayesian statistics is discussed.
The posterior distribution is complicated, but inference
can nevertheless be carried out via simulation, and some exact
formulae are derived for the case of random means.
The class of nonparametric priors provides an instructive example
where the speed with which the posterior forgets its prior
with increasing data sample size depends on special aspects of the prior,
which is a different situation from that of parametric inference.
Key words:
consistency,
Dirichlet process,
jump sizes,
nonparametric Bayes,
random means,
speed of memory loss,
stochastic equation
A postscript version of the entire preprint.