Consider the Bayesian linear model yi ~ N(x; B, o' ), i = 1, ...,n, n n n where Cri=0, =n and E Tiyi = 7- i=1 i=1 i=1 The prior for B and the dummy variable z is given by TT(B|z) = (1 - z)do(B) + zN(B|0, 72) and 7(z) = q'(1 -q)1-z. Suppose o, T and q are all known and do(B) is the indicator function which is 1 when B = 0 and is 0 otherwise. So, B = 0 if z = 0 and B = N(0, 72) if z = 1