9. Suppose we are estimating a set of residuals ri using a Monte Carlo approach, as described in Section 4.3. Due to a small sample size n, we are concerned that the approximation E(yi|y(i)) = 

E(yi|θ)p(θ|y(i))dθ ≈



E(yi|θ)p(θ|y)dθ

will not be accurate. A faculty member suggests the importance sampling estimate E(yi|y(i)) = 

E(yi|θ)

p(θ|y(i))

p(θ|y) p(θ|y)dθ

≈ 1 G



G g=1 E(yi|θ(g)

)

p(θ(g)

|y(i))

p(θ(g)

|y)

as an alternative. Is this a practical solution? What other approaches might we try? (Hint: See equation (3.4).)