Consider two independent q q Wishart matrices S1 W( 1A) and S2 W( 2A) where 1 = h and 2 = (1 )h for some h > q 1 and

(01)

What is the distribution of S = S1 +S2?

Use Corollary 2 of Dawid (1981) to show that S1 = U U where U satis es S = UU and has the matrix beta distribution Be( h2 (1 )h2)

Use the above result to verify the matrix beta evolution of precision matrices of Section 10.4.3.

Further, use the direct identity S = S1+S2 and the implied construc tion of p(SS1) to simply verify the retrospective ltering theory of Equation (10.12).