12.6 Bayesian Methods: 12.6.1 Predictive Densities, 12.6.2 Bayesian Prediction, 12.6.3 Bayesian Model Averaging

Verify (12.65). Hint: Use the partitioned matrix inverse formula A.9.1 and multiply out the quadratic form.

Find the form of the posterior predictive density for straight-line regression. Assume that the explanatory variable has been centered and that the prior mean is zero. Also assume that you are predicting a single value (i.e., assume that $m = 1$).