4. Suppose you have a Normal linear regression model with partially informative natural conjugate prior, where prior information is available only on J  k linear combinations of the regression coefficients, and the prior for h is the noninformative one of (3.24). Thus, Rþjh ¾ N.r; h
1Vr /, where R and r are defined after (3.25) and Vr is a J ð J positive definite matrix. Show that the posterior is given by

þ; hjy ¾ NG.eþ; eV ;es
2;e¹/

where eV D .R0V
1 r R C X0X/
1 eþ D eV.R0V
1 r þ C X0Xbþ/

e¹ D N and e¹es2 D ¹s2 C .eþ
bþ/0X0X.eþ
bþ/ C .Rbþ
r /0V
1 r .Rbþ
r /