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Bayesian Model Selection

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Bayesian Model Selection Reversible Jump MCMC Dimension of the model Classical statistical models and most Bayesian models assume a fixed size of the model Ex: AR ... – PowerPoint PPT presentation

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Title: Bayesian Model Selection


1
Bayesian Model Selection
  • Reversible Jump MCMC

2
Dimension of the model
  • Classical statistical models and most Bayesian
    models assume a fixed size of the model
  • Ex AR sequence with fixed model
  • N is assumed fixed
  • Ex2 source separation
  • The number of sources is assumed to be known
    beforehand
  • Ex3 DOA estimation (direction of arrival)
  • The number of arriving signals are assumed to be
    known

3
  • What if we do not know the model dimension
    beforehand?
  • And we would like to estimate the dimension as
    well.
  • The solution is an extension of MCMC, namely
    reversible jump MCMC (RJMCMC)

4
Ordinary Metropolis-Hastings MCMC
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example
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Bayesian mixture models
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Hierarchical model
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Univariate normal mixtures
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A
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Other applications
  • Image segmentation

Z. Kato, 2006, Image Vision Comput. 24 (10)
1103-1114 Oct 1 2006.
26
  • A more formal treatment can be found in
  • P. Green 1995 Reversible jump Markov chain Monte
    Carlo computation and Bayesian model
    determination, Biometrika, 82, 711-732 (1995).
  • Look also at the website of Peter Green.
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