1.

(a) Section 6.2 contains results for the Normal linear regression model with error covariance matrix
using the independent Normal-Gamma prior of

(6.9) and (6.10). Show how posterior results would change if the natural conjugate Normal-Gamma prior of Chapter 3, Section 3.4 were used for

þ and h.

(b) Using your result from part (a), show how posterior simulation in the heteroskedastic model of Section 6.3 would be altered if the natural conjugate Normal-Gamma prior were used.

(c) Using your result from part (a), show how posterior simulation in the regression model with Student-t errors of Section 6.4 would be altered if the natural conjugate Normal-Gamma prior were used.

(d) Using your result from part (a), show how posterior simulation in the regression model with autoregressive errors of Section 6.5 would be altered if the natural conjugate Normal-Gamma prior were used.