Bayesian Inference Using Artificial Augmenting Regressions

Abstract

In this article, it is shown that many intractable problems of Bayesian inference can be cast in a form called “artificial augmenting regression” in which application of Markov Chain Monte Carlo techniques, especially Gibbs sampling with data augmentation, is rather convenient. The new techniques are illustrated using several challenging statistical problems and numerical results are presented.

Keywords:

• Bayesian inference
• Extreme values
• Gibbs sampling
• Markov Chain Monte Carlo
• Pareto distributions
• Regression
• Stable distributions

Mathematics Subject Classification:

• Primary 62F15, 60G70, 60E07
• Secondary 65C05

Acknowledgments

The author wishes to thank an anonymous referee for many useful comments on an earlier version. The usual disclaimer applies.

Notes

¹For an excellent survey, see Geweke (1999).

² In a large number of artificially generated data with widely differing parameter values, 15 points have been found more than adequate.

³ It is well known that the Cauchy distribution in the previous section is a member of the class of stable distributions. The standard reference for stable distributions is Zolotarev (1986).