instead of being bounded by the values between 0 and 1. So the full conditional is developed for

the parameter q, the variable under the transformation, instead of r, for computational

advantages:


 7 = In -> r = -
 lnl-ry l+e"
 I (r e I +' e
 P(7) Pr e-





 (l+e")2 J














 Let
 P (7 |.) oc P ( ) (w ,r )
 1=1

 P(rl | )c e [ C n 1-fw-1 -1
 P+07 e 7 71 2

 I+e )r

Full conditional for N, :

 P(N, |.)oc f(w,. T,r,N, )g(N, A)2)

 PK | *)Tc, [I (I- r) (I- r) -w' e
 Let


(2-9)


 h(wi r, ) = f(w, T, r, k)(N, A)
 k=O
 P(N f(w. T,r,N,)g(N, I ) (2-10)
 h(w,. I, A)

 Where N, = 0, 1, 2, .... to K, when w,.= 0 and N, = 1, 2, ... to K, when w,.>1.

 The Gibbs sampler algorithm involves sampling random values sequentially from these

full conditionals. Each sample is drawn from the full conditional of a parameter using the

updated values of each of the other parameters. When this process is repeated arbitrarily a large