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On Expectation Propagation and the Probabilistic Editor in some simple mixture problems

Nils Lid Hjort, Mike Titterington

TL;DR

The paper identifies a few mixture problems in which Expectation Propagation and variations lead to approximate posterior distributions that asymptotically exhibit `correct'variances and therefore stand to provide reliable interval estimates for the unknown parameter or parameters.

Abstract

As for other latent-variable problems, exact Bayesian analysis is typically not practicable for mixture problems and approximate methods have been developed. Variational Bayes tends to produce approximate posterior distributions for parameters that are too tightly concentrated in having variances that are too small. The paper identifies a few mixture problems in which Expectation Propagation and variations thereof lead to approximate posterior distributions that asymptotically exhibit `correct' variances and therefore stand to provide reliable interval estimates for the unknown parameter or parameters.

On Expectation Propagation and the Probabilistic Editor in some simple mixture problems

TL;DR

The paper identifies a few mixture problems in which Expectation Propagation and variations lead to approximate posterior distributions that asymptotically exhibit `correct'variances and therefore stand to provide reliable interval estimates for the unknown parameter or parameters.

Abstract

As for other latent-variable problems, exact Bayesian analysis is typically not practicable for mixture problems and approximate methods have been developed. Variational Bayes tends to produce approximate posterior distributions for parameters that are too tightly concentrated in having variances that are too small. The paper identifies a few mixture problems in which Expectation Propagation and variations thereof lead to approximate posterior distributions that asymptotically exhibit `correct' variances and therefore stand to provide reliable interval estimates for the unknown parameter or parameters.
Paper Structure (24 sections, 93 equations)

This paper contains 24 sections, 93 equations.

Table of Contents

  1. Introduction
  2. Overview of the recursive-based approach to be adopted
  3. A general finite normal mixture with an unknown mean parameter
  4. Preamble
  5. The recursive step
  6. Fisher information
  7. Precision afforded by the complete-data scenario
  8. Variational Bayes approximation
  9. A symmetric mixture of two Gaussians
  10. Quasi-Bayes
  11. Confirmed-data case
  12. Minka's clutter problem
  13. Preamble
  14. Mixture of two known distributions
  15. Preamble
  16. ...and 9 more sections