Table 1.

Bayesian predictive probability approach: A schema and an example.

A. Schema
Y=i	Prob(Y=i | x)	Bi=Prob(P>p0 | x, Y=i)	Ii(Bi> θT)
0	Prob(Y=0 | x)	B0=Prob(P>p0 | p, f(p|x, Y=0))	0
1	Prob(Y=0 | x)	B1=Prob(P>p0 | p, f(p|x, Y=1))	0
…	…	…	…
m-1	Prob(Y=m-1| x)	Bm-1 =Prob(P>p0 | p, f(p|x, Y=m-1))	1
m	Prob(Y=m | x)	Bm =Prob(P>p0 | p, f(p|x, Y=m))	1

B. Example: Nmax = 40, x = 16, n = 23, prior distribution of P ~ beta(0.6, 0.4)
Y=i	Prob(Y=i | x)	Bi=Prob(P>60% | x, Y=i)	Ii(Bi>0.90)
0	0.0000	0.0059	0
1	0.0000	0.0138	0
2	0.0001	0.0296	0
3	0.0006	0.0581	0
4	0.0021	0.1049	0
5	0.0058	0.1743	0
6	0.0135	0.2679	0
7	0.0276	0.3822	0
8	0.0497	0.5085	0
9	0.0794	0.6349	0
10	0.1129	0.7489	0
11	0.1426	0.8415	0
12	0.1587	0.9089	1
13	0.1532	0.9528	1
14	0.1246	0.9781	1
15	0.0811	0.9910	1
16	0.0381	0.9968	1
17	0.0099	0.9990	1