In the context of selection of number of factors of Section 11.2.6, show that the integrated likelihood function for the parameters of the k-factor model obtained by integrating out the latent factor vectors x1 xn is given by (Lopes and West 2004)

p(yk k)=(2 ) nr 2BHB+V n2exp 1 2

n i=1 yi(BHB+V) 1yi