... I)dθ(1).Using Bayes rule (45 ) is the same as ( 47 )pθ∗(1)| I2pθ(2)| θ∗(1),Iuθ∗(2)| θ∗(1), θ(2),H2dθ(2).Carrying out the integration in (46 ) yields (48 )pθ∗(2)| ... θ∗(1), θ∗(2),H2and so ( 47 ) becomes (49 )pθ∗(1)| Ipθ∗(2)| θ∗(1),I2uθ(2)| θ∗(1), θ∗(2),H2dθ(2).We can express (48 ) as(50)pθ∗(1), θ∗(2)| ... θ∗(2)| Irθ∗(2)| θ∗(1),H2.Finally, recalling (43 ),thesumof (49 ) and (50) is p(θ∗(1), θ∗(2)| I), thus establish-ing (44 ).This demonstration of invariance applies to the Gibbs...