Abstract
SUMMARY A formal Bayesian analysis of a mixture model usually leads to intractable calculations, since the posterior distribution takes into account all the partitions of the sample. We present approximation methods which evaluate the posterior distribution and Bayes estimators by Gibbs sampling, relying on the missing data structure of the mixture model. The data augmentation method is shown to converge geometrically, since a duality principle transfers properties from the discrete missing data chain to the parameters. The fully conditional Gibbs alternative is shown to be ergodic and geometric convergence is established in the normal case. We also consider non-informative approximations associated with improper priors, assuming that the sample corresponds exactly to a k-component mixture.
Keywords
Bayesian probabilityMathematicsStatisticsSampling (signal processing)EstimationBayes estimatorComputer scienceApplied mathematicsEngineering
Affiliated Institutions
Related Publications
Practical Bayesian Density Estimation Using Mixtures of Normals
Abstract Mixtures of normals provide a flexible model for estimating densities in a Bayesian framework. There are some difficulties with this model, however. First, standard ref...
Variable Selection via Gibbs Sampling
Abstract A crucial problem in building a multiple regression model is the selection of predictors to include. The main thrust of this article is to propose and develop a procedu...
Applied Missing Data Analysis
Part 1. An Introduction to Missing Data. 1.1 Introduction. 1.2 Chapter Overview. 1.3 Missing Data Patterns. 1.4 A Conceptual Overview of Missing Data heory. 1.5 A More Formal De...
Markov Chain Monte Carlo Methods and the Label Switching Problem in Bayesian Mixture Modeling
In the past ten years there has been a dramatic increase of interest in the Bayesian analysis of finite mixture models. This is primarily because of the emergence of Markov chai...
A Split-Merge Markov chain Monte Carlo Procedure for the Dirichlet Process Mixture Model
This article proposes a split-merge Markov chain algorithm to address the problem of inefficient sampling for conjugate Dirichlet process mixture models. Traditional Markov chai...
Publication Info
- Year
- 1994
- Type
- article
- Volume
- 56
- Issue
- 2
- Pages
- 363-375
- Citations
- 904
- Access
- Closed
External Links
Social Impact
Altmetric
PlumX Metrics
Social media, news, blog, policy document mentions
Citation Metrics
904
OpenAlex
Cite This
Jean Diebolt,
Christian P. Robert
(1994).
Estimation of Finite Mixture Distributions Through Bayesian Sampling.
Journal of the Royal Statistical Society Series B (Statistical Methodology)
, 56
(2)
, 363-375.
https://doi.org/10.1111/j.2517-6161.1994.tb01985.x
Identifiers
- DOI
- 10.1111/j.2517-6161.1994.tb01985.x