1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
|
clear all
B0 = 1; Rtriple = 2; Damnio = 3;
B1 = 4; Ramnio = 5; Dabort = 6;
B2 = 7; U = 8;
N = 8;
dag = zeros(N,N);
dag(B0, [Rtriple B1 Ramnio]) = 1;
dag(Rtriple, [Damnio Dabort]) = 1;
dag(Damnio, [B1 Ramnio]) = 1;
dag(B1, B2) = 1;
dag(Ramnio, [Dabort U]) = 1;
dag(Dabort, B2) = 1;
dag(B2, U) = 1;
ns = zeros(1,N);
ns(B0) = 2;
ns(B1) = 3;
ns(B2) = 4;
ns(Rtriple) = 2;
ns(Ramnio) = 3;
ns(Damnio) = 2;
ns(Dabort) = 2;
ns(U) = 1;
limid = mk_limid(dag, ns, 'chance', [B0 B1 B2], ...
'decision', [Damnio Dabort], 'utility', [U]);
% states of nature
healthy = 1; downs = 2; miscarry = 3; aborted = 4;
% test results
pos = 1; neg = 2; unk = 3;
% actions
yes = 1; no = 2;
% Prior probability baby has downs syndrome
tbl = zeros(2,1);
p = 1/1000; % from www.downs-syndrome.org.uk figure
p = 24/10000; % www-personal.umich.edu/~bobwolfe/560/review/Downs.pdf (for women agen 35-40)
tbl(healthy) = 1-p;
tbl(downs) = p;
limid.CPD{B0} = tabular_CPD(limid, B0, tbl);
% Reliability of triple screen test
% Unreliable sensor
% B0 -> Rtriple
tbl = zeros(2,2); % Rtriple = pos, neg
p = 0.5; % high false positive rate (guess)
tbl(healthy, :) = [p 1-p];
p = 0.6; % low detection rate (march of dimes figure)
tbl(downs, :) = [p 1-p];
limid.CPD{Rtriple} = tabular_CPD(limid, Rtriple, tbl);
limid.CPD{Damnio} = tabular_decision_node(limid, Damnio);
% Effect of amnio on baby B0,Damnio -> B1
% 1/200 risk of miscarry
p = 1/200; % (march of dimes figure)
tbl = zeros(2, 2, 3); % B1 = healthy, downs, miscarry
tbl(healthy, no, :) = [1 0 0];
tbl(downs, no, :) = [0 1 0];
tbl(healthy, yes, :) = [1-p 0 p];
tbl(downs, yes, :) = [0 1-p p];
limid.CPD{B1} = tabular_CPD(limid, B1, tbl);
% Reliability of amnio B0, Damnio -> Ramnio
% Perfect sensor
tbl = zeros(2,2,3); % Ramnio = pos, neg, unk
tbl(:, no, :) = repmat([0 0 1], 2 ,1);
tbl(healthy, yes, :) = [0 1 0];
tbl(downs, yes, :) = [1 0 0];
limid.CPD{Ramnio} = tabular_CPD(limid, Ramnio, tbl);
limid.CPD{Dabort} = tabular_decision_node(limid, Dabort);
% Effect of abortion on baby B1, Dabort -> B2
tbl = zeros(3, 2, 4); % B2 = healthy, downs, miscarry, aborted
tbl(:, yes, :) = repmat([0 0 0 1], 3, 1);
tbl(healthy, no, :) = [1 0 0 0];
tbl(downs, no, :) = [0 1 0 0];
tbl(miscarry, no, :) = [0 0 1 0];
limid.CPD{B2} = tabular_CPD(limid, B2, tbl);
% Utility U(Ramnio, B2)
tbl = zeros(3, 4);
tbl(:, healthy) = 5000;
tbl(:, downs) = -50000;
tbl(:, miscarry) = -1000;
tbl(:, aborted) = -1000;
if 0
%tbl(unk, miscarry) = 0; % this case is impossible
tbl(pos, miscarry) = -1;
tbl(neg, miscarry) = -1000;
if 1
tbl(unk, aborted) = -100;
tbl(pos, aborted) = -1;
tbl(neg, aborted) = -500;
else % pro-life utility fn
tbl(unk, aborted) = -500000;
tbl(pos, aborted) = -500000;
tbl(neg, aborted) = -500000;
end
end
limid.CPD{U} = tabular_utility_node(limid, U, tbl);
engine = jtree_limid_inf_engine(limid);
[strategy, MEU] = solve_limid(engine);
% Rtriple U(Damnio=1=yes) U(Damnio=2=no)
% 1=pos 0 1
% 2=neg 0 1
dispcpt(strategy{Damnio})
if isequal(strategy{Damnio}(1,:), strategy{Damnio}(2,:))
% Rtriple result irrelevant
doAmnio = argmax(strategy{Damnio}(1,:))
else
doAmnio = 1;
end
% Rtriple Ramnio U(Dabort=yes=1) U(Dabort=no=2)
% 1=pos 1=pos 1 0
% 2=neg 1=pos 1 0
% 1=pos 2=neg 0 1
% 2=neg 2=neg 0 1
% 1=pos 3=unk 0 1
% 2=neg 3=unk 0 1
dispcpt(strategy{Dabort})
|
