For the simple univariate regression model of Section 12.2. I suppose that instead of asuming the u,s are independent, we assume serially correlated errors with corr(u,u,) = p , i # j , var(u,) = cr2, 0 < p c 1. Adopt a vague prior for (p,, &, &), assume p is u priori independent of (PI, /I2, d), and assume a uniform prior for p on the unit interval.

(a) Find the joint posterior density for (/?,, /I2, d,p) .

(b) Find the marginal posterior density for p.

(c) Find the marginal posterior density for /I2.

(d) Find the marginal posterior density for $.

(e) Find the predictive density for a new observation y* based upon a new