3.11 ( ) We have seen that, as the size of a data set increases, the uncertainty associated with the posterior distribution over model parameters decreases. Make use of the matrix identity (Appendix C)

M+ vvT−1 = M−1 −

(M−1v)

vTM−1 1 + vTM−1v

(3.110)

to show that the uncertainty σ2N

(x) associated with the linear regression function given by (3.59) satisfies

σ2N

+1(x)
σ2N

(x). (3.111)