Cauchy Priors: Mixtures of Normals & MCMC
Abstract
In this lecture we will go show how Cauchy priors can be derived as a mixture of normal distributions and introduce MCMC sampling for estimation.
Readings: Christensen Chapter 2 and Chapter 6, Appendix A & B as needed C Hoff Ch 9.
In this lecture we will look at potential problems with conjugate Normal prior distriubtions and show how they can be “robustified” by developing scale mixtures of Normal distributions, in particular, the Cauchy prior recommended by Zellner & Siow (1980).
Zellner, A., & Siow, A. (1980). Posterior odds ratios for selected regression hypotheses. In J. M. Bernardo, M. H. DeGroot, D. V. Lindley, & A. F. M. Smith (Eds.), Bayesian statistics: Proceedings of the First International Meeting held in Valencia (Spain) (pp. 585– 603). Valencia, Spain: University Press.
