For the three link functions of identify the latent variable structure z identifying y as the indicator
Consider a posterior distribution 
such that the three full conditional distributions 
are available.
a. Show that
b. Show that 
can be approximated by
where the 
are generated by Gibbs sampling.
c. Show that 
can be approximated by
where the 
are generated by Gibbs sampling from the conditional distributions 
that is, with θ1 being kept equal to θˆ1.
d. Extend to the case where p full conditional distributions are available and evaluate the computing cost of this approximation method.
