Finding sets of parameters

Question

Solve the following problem:

The witch's hat distribution

π(θ|y) ∝ {(1- δ)σ^-de^{-||y-θ||2/(2σ2)} + δ}IIC(θ),   y∈R^d,

a. Construct an algorithm that correctly simulates the witch's hat distribution. (Hint: Show that direct simulation is possible.)

b. The choice of δ, σ, and d can lead to arbitrarily small probabilities of either escaping the attraction of the mode or reaching it. Find sets of parameters (δ, σ, y) for whichbthese two phenomena occur.

c. In each case, test the various convergence diagnoses proposed by coda to check whether or not they notice the difficulty.