Response to the following problem:
(Berger et al., 1998) For a p × p positive-definite symmetric matrix Σ, consider the distribution
π(θ) ∝ exp (-(θ - μ)t ∑-1 (θ - μ)/2) / ||θ||P-1
a. Show that the distribution is well-defined; that is, ?Rp π(θ)dθ
b. Show that an importance sampling implementation based on the normal instrumental distribution Np(μ, Σ) is not satisfactory from both theoretical and practical points of view.
c. Examine the alternative based on a gamma distribution G(α, β) on η = ||θ||2 and a uniform distribution on the angles.