Richardson and Green present a method of performing a Bayesian
analysis of data from a finite mixture distribution with an unknown number of
components. Their method is a Markov Chain Monte Carlo (MCMC) approach, which
makes use of the “reversible jump” methodology described by
Green. We describe an alternative MCMC method which views the parameters of the
model as a (marked) point process, extending methods suggested by Ripley to
create a Markov birth-death process with an appropriate stationary
distribution. Our method is easy to implement, even in the case of data in more
than one dimension, and we illustrate it on both univariate and bivariate data.
There appears to be considerable potential for applying these ideas to other
contexts, as an alternative to more general reversible jump methods, and we
conclude with a brief discussion of how this might be achieved.
Publié le : 2000-02-14
Classification:
Bayesian analysis,
birth-death process,
Markov process,
MCMC,
mixture model,
model choice,
reversible jump,
spatial point process,
62F15
@article{1016120364,
author = {Stephens, Matthew},
title = {Bayesian analysis of mixture models with an unknown number of
components---an alternative to reversible jump methods},
journal = {Ann. Statist.},
volume = {28},
number = {3},
year = {2000},
pages = { 40-74},
language = {en},
url = {http://dml.mathdoc.fr/item/1016120364}
}
Stephens, Matthew. Bayesian analysis of mixture models with an unknown number of
components—an alternative to reversible jump methods. Ann. Statist., Tome 28 (2000) no. 3, pp. 40-74. http://gdmltest.u-ga.fr/item/1016120364/