Bayesian analysis of mixture models with an unknown number of components—an alternative to reversible jump methods
Top Cited Papers
Open Access
- 1 February 2000
- journal article
- Published by Institute of Mathematical Statistics in The Annals of Statistics
- Vol. 28 (1) , 40-74
- https://doi.org/10.1214/aos/1016120364
Abstract
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.Keywords
This publication has 28 references indexed in Scilit:
- Markov Chain Monte Carlo Convergence Diagnostics: A Comparative ReviewJournal of the American Statistical Association, 1996
- Reversible jump Markov chain Monte Carlo computation and Bayesian model determinationBiometrika, 1995
- Marginal Likelihood from the Gibbs OutputJournal of the American Statistical Association, 1995
- Bayesian Density Estimation and Inference Using MixturesJournal of the American Statistical Association, 1995
- Adaptive MixturesJournal of the American Statistical Association, 1994
- An Application of the Laplace Method to Finite Mixture DistributionsJournal of the American Statistical Association, 1994
- Inference from Iterative Simulation Using Multiple SequencesStatistical Science, 1992
- Density Estimation with Confidence Sets Exemplified by Superclusters and Voids in the GalaxiesJournal of the American Statistical Association, 1990
- Probes of large-scale structure in the Corona Borealis regionThe Astronomical Journal, 1986
- Time reversible and Gibbsian point processes I. Markovian spatial birth and death processes on a general phase spaceMathematische Nachrichten, 1981