21. Bayesian Regression Analysis

  1. Reinhard Viertl

Published Online: 5 JAN 2011

DOI: 10.1002/9780470974414.ch21

Statistical Methods for Fuzzy Data

Statistical Methods for Fuzzy Data

How to Cite

Viertl, R. (2011) Bayesian Regression Analysis, in Statistical Methods for Fuzzy Data, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9780470974414.ch21

Author Information

  1. Vienna University of Technology, Austria

Publication History

  1. Published Online: 5 JAN 2011
  2. Published Print: 11 FEB 2011

ISBN Information

Print ISBN: 9780470699454

Online ISBN: 9780470974414

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Keywords:

  • Bayesian regression analysis;
  • a posteriori distribution calculation;
  • Bayes' theorem;
  • Bayesian confidence regions;
  • posteriori distribution - constructing Bayesian confidence regions;
  • highest a posteriori density regions, or HPD-regions - for parameter vector;
  • probabilities of hypotheses;
  • predictive distributions - elegant way of using a posteriori distribution;
  • a posteriori Bayes estimators - for regression parameters;
  • Bayesian regression - with Gaussian distributions

Summary

This chapter contains sections titled:

  • Calculation of a posteriori distributions

  • Bayesian confidence regions

  • Probabilities of hypotheses

  • Predictive distributions

  • A posteriori Bayes estimators for regression parameters

  • Bayesian regression with Gaussian distributions

  • Problems