Mixtures
Wiley series in probability and statisticsPublished 15 April 2011
Citations96
Generate an AI Snapshot to get a quick, structured summary of this paper.
Study Snapshot
ObjectiveStudy objective
MethodsResearch methodology
PopulationPopulation studied
Sample sizeSample sizes
OutcomesStudy outcomes here
ResultsStudy results comes here
LimitationsResearch study limitations comes here
A concise AI-generated summary of the paper will appear here once you click Generate AI Snapshot.
Abstract
In this paper, we show how a complete and exact Bayesian analysis of a parametric mixture model is possible in some cases when components of the mixture are taken from exponential families and when conjugate priors are used.This restricted set-up allows us to show the relevance of the Bayesian approach as well as to exhibit the limitations of a complete analysis, namely that it is impossible to conduct this analysis when the sample size is too large, when the data are not from an exponential family, or when priors that are more complex than conjugate priors are used.
Keywords
ChemistryChemical Engineering
Springer texts in statisticsMonte Carlo Statistical Methods
4,050 Citations2004Christian P. Robert, George Casella
Journal of the Royal Statistical Society Series B (Statistical Methodology)On Bayesian Analysis of Mixtures with an Unknown Number of Components (with discussion)
1,913 Citations1997Sylvia Richardson, Peter J. Green
Springer series in statisticsFinite Mixture and Markov Switching Models
1,591 Citations2006Sylvia Frühwirth‐Schnatter
This book should help newcomers to the field to understand how finite mixture and Markov switching models are formulated, what structures they imply on the data, what they could be used for, and how they are estimated.
Journal of the Royal Statistical Society Series B (Statistical Methodology)Dealing With Label Switching in Mixture Models
1,088 Citations2000Matthew Stephens
It is demonstrated that this fails in general to solve the ‘label switching’ problem, and an alternative class of approaches, relabelling algorithms, which arise from attempting to minimize the posterior expected loss under a class of loss functions are described.
Statistical ScienceMarkov Chain Monte Carlo Methods and the Label Switching Problem in Bayesian Mixture Modeling
673 Citations2005Ajay Jasra, Chris Holmes +1 more
The solutions to the label switching problem of Markov chain Monte Carlo methods, such as artificial identifiability constraints, relabelling algorithms and label invariant loss functions are reviewed.
Journal of the American Statistical AssociationPractical Bayesian Density Estimation Using Mixtures of Normals
105 Citations1997Kathryn Roeder, Larry Wasserman
Journal of the American Statistical AssociationEstimating a Product of Means: Bayesian Analysis with Reference Priors
83 Citations1989James O. Berger, José M. Bernardo
Computational Statistics & Data AnalysisBayesian model choice based on Monte Carlo estimates of posterior model probabilities
78 Citations2004Peter Congdon
An approach is outlined here that produces posterior model probabilities and hence Bayes factor estimates but not marginal likelihoods and uses a Monte Carlo approximation based on independent MCMC sampling of two or more different models.
Statistical MethodologyMixture models, latent variables and partitioned importance sampling
38 Citations2004George Casella, Christian P. Robert +1 more
An alternative approach to estimation in mixture models is examined, one based on a Rao–Blackwellization argument applied to a latent-variable-based estimator, and an alternative Monte Carlo sampling scheme is constructed that avoids trapping states.
arXiv (Cornell University)Bayesian Inference on Mixtures of Distributions
37 Citations2008Kate Lee, Jean‐Michel Marin +2 more
This survey covers state-of-the-art Bayesian techniques for the estimation of mixtures by studying new types of distributions, the multinomial, latent class and t distributions and sheds a new light on the computation of Bayes factors via the approximation of Chib (1995).
Statistics and ComputingDirect simulation for discrete mixture distributions
17 Citations2005Paul Fearnhead
The approach is based on directly calculating the posterior distribution using a set of recursions which are similar to those of the Forward-Backward algorithm, which is more practicable than existing perfect simulation methods for mixtures.