3.7 Consider the average value of the function G(B) with respect to the posterior distribution of the unobservable 8, based upon a set of continuous data:

x , , . . . ,x,. The average G is given by:

where h denotes the posterior pdf, L denotes the likelihood function, and g Cenotes the prior pdf. Suppose G denotes the squared diffe!ence between 8 and 8, an estimate of it, based upon the data. Find the value of 0 that minimizes this E[G(O)]. (See Chapter 11 for a more general discussion of this problem.) Note that such integrals can be approximated by the Laplace approximation discussed in Section 7.3.2.