13.4 Consider an improper prior distribution for jl and y given 02:p(By,y )

proportional to I gX& lo?

(a) What happens to the prior distribution of p, if g is multiplied by an arbitrary constant?

(b) Find the posterior distribution for f i r . What happens to the posterior distribution for /3, if g is multiplied by an arbitrary constant?

(c) Find the posterior distribution of y. What happens to the posterior distribution of y when p is multiplied by an arbitmry constant’?

(d) If tha prior distribution is p(& y ) o(

c, where c does not depend on the data, show that the posterior model probabilities are not invariant to scale changes in X.