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