5. In Example 8.7 (gas demand), consider the option where t follows a Student t obtained via a scale mixture with degrees of freedom

5. In Example 8.7 (gas demand), consider the option where εt follows a Student t obtained via a scale mixture with degrees of freedom ν set at 5. So weights wt (reducing the precision 1/σ 2) are obtained from a gamma density Ga(2.5, 2.5). Compare the predictive loss criterion C(k) (see Section 2.6 and Equation (6) in Gelfand and Ghosh, 1998) for this model and the two models already considered. This criterion is

where var(ynew) and E(ynew) are obtained over a large number of MCMC iterations; try k = 1 and k = 1000. Does allowing ν to be a free parameter improve C(k) for the scale mixture option?

C(k) = var(ynew.i) + [k/(k+1)] {E(ynew.i) - yi), i=1 i=1