Exercise 9.14 Gelman (2006) suggested to reformulate the Gaussian hierarchical model as yi j ∼ N(µ + ξ ηi, σ2 ) ξ ∼ N(0, σ2 η ).

In WinBUGS program ‘chapter 9 dietary study chol folded.odc’ the original IBBENS data are analyzed according to the above model with a half-Cauchy prior with scale parameter 25 for σθ using a N(0, 52 ) prior on ξ and an IG(0.5, 0.5)-prior for σ2 η . Replay the analysis and vary the parameters of the priors to examine their impact on the posterior p(σθ | y). In Gelman (2006), it is claimed that the above reformulation of the Gaussian hierarchical model reduces the autocorrelation of the sampled parameters. Verify this on the behavior of σθ .