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Mixture Models

  • Jean-Michel Marin
  • Christian P. Robert
Chapter
Part of the Springer Texts in Statistics book series (STS)

Abstract

This chapter covers a class of models where a rather simple distribution is made more complex and less informative by a mechanism that mixes together several known or unknown distributions. This representation is naturally called a mixture of distributions, as illustrated above. Inference about the parameters of the elements of the mixtures and the weights is called mixture estimation, while recovery of the original distribution of each observation is called classification (or, more exactly, unsupervised classification to distinguish it from the supervised classification to be discussed in Chap. 8).

Keywords

Posterior Distribution Gibbs Sampler Marginal Likelihood Dirichlet Process Label Switching 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Chib, S. (1995). Marginal likelihood from the Gibbs output. J. American Statist. Assoc., 90:1313–1321.MathSciNetCrossRefMATHGoogle Scholar
  2. Frühwirth-Schnatter, S. (2006). Finite Mixture and Markov Switching Models. Springer-Verlag, New York, New York.MATHGoogle Scholar
  3. Gelfand, A. and Dey, D. (1994). Bayesian model choice: asymptotics and exact calculations. J. Royal Statist. Society Series B, 56:501–514.MathSciNetMATHGoogle Scholar
  4. Green, P. (1995). Reversible jump MCMC computation and Bayesian model determination. Biometrika, 82(4):711–732.MathSciNetCrossRefMATHGoogle Scholar
  5. Hjort, N., Holmes, C., Müller, P., and Walker, S. (2010). Bayesian Nonparametrics. Cambridge University Press, Cambridge.CrossRefMATHGoogle Scholar
  6. Marin, J.-M. and Robert, C. (2007). Bayesian Core. Springer-Verlag, New York.MATHGoogle Scholar
  7. Robert, C. and Casella, G. (2004). Monte Carlo Statistical Methods. Springer-Verlag, New York, second edition.Google Scholar
  8. Tanner, M. (1996). Tools for Statistical Inference: Observed Data and Data Augmentation Methods. Springer-Verlag, New York, third edition.Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Jean-Michel Marin
    • 1
  • Christian P. Robert
    • 2
  1. 1.Université Montpellier 2MontpellierFrance
  2. 2.Université Paris-DauphineParisFrance

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