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Takahisa Hirokawa 08N8100030C
2010 3
i
2
2
ii
1 ........................................................................................................................1
1.1 .........................................................................................................1
1.2 .............................................................................................................2
2 .............................................................................................................3
2.1 .......................................................................................3
2.1.1 ...............................................................................................4
2.1.2 .............................................................................................................7
2.1.3 ......................................................................................................8
2.2 ..................................................................................10
2.2.1 ..................................................................................10
2.2.2 1 ...................................................................................... 11
2.2.3 ........................................................................13
2.2.4 .............................................................15
3 ......................................................................................18
3.1 .........................................................................................18
3.2 .................................................19
3.2.1 .................................................................................................19
3.2.2 ...........................................................................................................21
3.3 ..................................................................................................................23
3.3.1 ....................................................................................................24
3.2.2 Junction Tree .......................................................................................26
3.3.3 Junction Tree ..............................................................30
3.4 Bayes Net Toolbox ....................................................................................................31
4 .......................................32
4.1 .......................................................................................................32
4.1.1 Dijkstra ..........................................................................................................32
4.1.2 .................................................................................................33
4.2 2 ..........................................33
4.2.1 ........................................................................................................34
iii
4.2.2 .................................................................................................48
4.2.3 ...........................................49
4.2.4 .........................................................50
4.2.5 CPT ........................................................................................................56
4.2.6 ...........................................................................................................59
4.3 ..........................................................................62
4.3.1 ........................................................................................................62
4.3.2 ...........................................65
4.3.3 ...........................................................................................................67
5 ......................................................................................................................72
5.1 .....................................................................................................................72
5.2 ..............................................................................................................75
....................................................................................................................................76
.............................................................................................................................77
.............................................................................................................................78
A 2 CPT..........79
B CPT ...............................84
1
1
1.1
2
2
[5]
2
8 8 2
8 2
2
15
[8]
1.2
2
3
4
2
3
2
2.1
2005 9 29 78 10 2 81
159
2 16
3
4
2.1.1
2005 9 29 78 2005 10 2
81
[ ]
2.1 20 30
30
2.1
2.2
2.2
5
2.3
2
2.3
2.4
3
3
2.4
6
2.5 30
20.6
24.1
2.5
2.6
3
2.6
7
2.1.2
3 2.1
2.1
22
18
15
GAP 12
8
5
Afternoon Tea 4
ABC 3
TSUTAYA 3
3
1 3
2 3
2.7 5
2.7 1
1 1.7
2.7
8
2.1.3
147
147 131
16
11
5 16
1 1
1
2
1
5 2.2
1 2
9
2.2
[ ]
27
24
GAP 24
22
15
2 15
1 14
9
Afternoon Tea 8
7
100 6
CAFE DENMARK 6
LAURA ASHLEY HOME 6
NEXT 6
OUTLET 5
FUJIYA BOOK 5
LAURA ASHLEY HOME 5
5
TSUTAYA 5
2.8
10 1 4
2.6
0 2.8
10
2.8
2.2
2
1
2.2.1
Mapple
Mapple
1/10000
[ m ]
[ m ] [ % ]
x y
Mapple 2600m
11
4669 6000 2.9 2.9
2.9
2.2.2 1
2.9 2
2.10 2.10
12
2.10
2 1
2
1
2.11 2.11 1
1 4606 5924
2.11 1
13
2.2.3
2.2.2 1
131
P yx PP , A yx AA , B yx BB , AB
)})(())()}{()(())({( xxxxyyyyxxxxyyyy BAPBBAPBBAPABAPAF (2.1)
F 0 P ABM x xM y
yM
2)(2)(
2)(2)())()((
yB
yA
xB
xA
yB
yA
xA
xB
xA
xP
xB
xA
yB
yA
yA
yP
xP
xM (2.2)
2)(2)(
2)(2)())()((
yB
yA
xB
xA
xB
xA
yA
yB
yA
yP
yB
yA
xB
xA
xA
xP
yP
yM (2.3)
P A B AB
M PM P
P M PM
AB AM MB PM 0
2.12
14
2.12
123 1
1 2 2 2
2
1 2 2
2
2
1 1 4 2 2
2
0 2.13 2.13
MPPM
MAAM
BMMB
BA M
BAAB
P
BA
P
15
2
2.13 2
2.2.4
2.2.3
2
1
131
4864 6185 2.14
1
1 1
1 22
2 1
16
2.14
1
2.14
17
2.1.3 2.2 10
2.15
2.15 10
12
GAP
Afternoon
Tea
18
3
3.1
DAG Directed Acyclic Graph
CPT Conditional Probability Table
3.1 Cloudy Rain
Sprinkler Wet grass
2 Sprinkler Rain 2 Cloudy
Cloudy Wet Grass
Sprinkler Rain 2 2
19
Cloudy
0.5P(Cloudy=T
0.5P(Cloudy=F
0.5P(Cloudy=T
0.5P(Cloudy=F
0.10.5P Sprinkler=T
0.90.5P Sprinkler=F
Cloudy=TCloudy=F
0.10.5P Sprinkler=T
0.90.5P Sprinkler=F
Cloudy=TCloudy=F
0.80.2P Rain=T
0.20.8P Rain=F
Cloudy=TCloudy=F
0.80.2P Rain=T
0.20.8P Rain=F
Cloudy=TCloudy=F
Sprinkler=TSprinkler=F
0.990.90.90.0P Wet Grass=T
0.010.10.11.0P Wet Grass=F
Rain=TRain=FRain=TRain=F
Sprinkler=TSprinkler=F
0.990.90.90.0P Wet Grass=T
0.010.10.11.0P Wet Grass=F
Rain=TRain=FRain=TRain=F
Sprinkler Rain
Wet Grass
3.1
3.2
CPT
CPT
3.2.1
20
n i iq
i ir
ijkN i j i k
3.2 3.1 6
CjkN 3.2
3.1
A B C
1 1a 1b 1c
2 1a 1b 2c
3 1a 2b 1c
4 2a 1b 1c
5 2a 2b 2c
6 2a 2b 2c
3.2 CjkN
1aA 1aA
1bB 2bB 1bB 2bB
1cC111 },{ cbBaACN =1
121 },{ cbBaACN =1112 },{ cbBaACN =1
122 },{ cbBaACN =0
2cC211 },{ cbBaACN =1
221 },{ cbBaACN =0212 },{ cbBaACN =0
222 },{ cbBaACN =2
ijk i j i k
ijkN ijk
3.1
ij
ijk
ijkN
N3.1
1
0
ir
kijkij NN 0ijN iijk r/1
CPT
C
A B
3.2
21
CPT
CPT
pseudo counts ijkN
ijkN ijkN ijkN
ijkN ijkˆ
3.2
ijij
ijkijk
ijkNN
NNˆ 3.2
1
0
ir
kijkij NN 0ijkN
i
irkqij iiN }1,,0{},,1{
ijkˆ
ijk ir/1 i CPT
i ijkˆ
ir/1
ijkN CPT
0ijkN
CPT
i
CPT ijkˆ
ijkˆ
3.2.2
1 K2 K2
K2
3.1
Cloudy Sprinkler Rain Wet Grass Cloudy Rain Sprinkler Wet Grass
2
22
3.3
3.3
1 1
2 3
3 25
4 543
5 29,281
6 3,781,503
7 9101.1
8 11108.7
9 15102.1
10 18102.4
n X },,,{ 21 nXXX
iX )( iXpa K2
Step 1 1i )( iXpa
Step 2 ))(|( jii XXpaXP jX 11 ij
ji XXpa )(
Step 3 ))(|( ii XpaXP ))(|( jii XXpaXP ))(|( ii XpaXP
Step3-1 ))(|( jii XXpaXP
Step3-2
Step 3-1 ni ni i 1 Step2
Step 3-2 )( iXpa ji XXpa )( Step2 },,,{)( 121 ii XXXXpa
i 1 Step2
K2
sB ijk
D D
23
),|( sBDp 6 3.3
n
i
q
j
r
k
N
ijk
r
k
N
ijk
n
i
q
jr
k
ijk
r
k
ijk
s
i i
ijk
i
ijk
i
i
i
N
N
BDp1 1
1
0
1
01 11
0
1
0
!
!
),|( 3.3
sB
),|( sBDpn
i
q
j
r
k
N
ijk
i iijk
1 1
1
0
),|(log sBDpn
i
q
j
r
kijkijk
i i
N1 1 0
1
log
D sB
sB3.4 )|( Dl
ss BB
n
i
q
j
r
k
ijkijkBB
i i
ssNDl
1 1 0
1
log)|( 3.4
)|( Dlss BB 3.4 sB
iX )( iXpa
)( iXpai iq
j
r
kijkijkN
1 0
1
log
BIC Bayesian information criterion
BIC
sB sBk
n
iiB qk
s1
N sB
BICsB
BIC 3.5
)(log)|(2 NkDlBICssss BBBB 3.5
BIC
3.3
1 evidence
evidence
3.1
, Wet grass = T evidence
Sprinkler
24
Junction Tree Junction Tree
Belief Propagation
Junction Tree
Junction Tree
Junction Tree
3.3.1
3.3.2 Junction Tree
3.3.3 Junction Tree
3.3.1
dom( )
)|,( CBAP dom },,{))|,(( CBACBAP
2
dom( 21 ) = dom( 1 ) dom( 2 )
1221
)()( 321321
1 1
1
A
A A dom ( A ) = dom A/)(
B AA B
)|(AP
1)|(A AP
25
A dom( 1 ) AA 2121
3.4 3.9 3.4 1
2 3.5 3.5 2
1c 2c 3.6 3.7
3.8
C BCBA ),(),( 21 = C BCBA ),(),( 21 3.7 3.8
3.4 ),(1 BA ),(2 BC
),(1 BA ),(2 BC
AB \ 1a 2a CB \ 1c 2c
1b 1x 2x 1b 1y 2y
2b 3x 4x 2b 3y 4y
3.5 ),(),( 21 BCBA
AB \ 1a 2a
1b 2111 , yxyx 2212 , yxyx
2b 4333 , yxyx 4434 , yxyx
3.6 C BC ),(2
B
1b 1y + 2y
2b 3y + 4y
3.7 C BCBA ),(),( 21
AB \ 1a 2a
1b 2111 yxyx 2212 yxyx
2b 4333 yxyx 4434 yxyx
3.8 C BCBA ),(),( 21
AB \ 1a 2a
1b )( 211 yyx )( 212 yyx
2b )( 433 yyx )( 434 yyx
26
),,( CBA A B C
C 3.6 C BC ),(2BBC ),(2
w
vwwv )()(
dom( 1 ) )()( 2121
Junction Tree
[ ] X X
Step 1 X
X
Step 2 X XX
Step 3 X X },\{ XX
X
X)( X
[ ] = )}(),,(),,(),,(,)({ 54321 CDCCABAA W = },{ CB W
)},(),,(),,(),({ 4321, DCCABAADAX
A D
A D
DA
X XX
DCCABAA
DCCABAA
DCCABAA
),(),(),()(
),(),(),()(
)},(),,(),,(),({
4321
4321
, 4321
}),(),(),()(),({
},\{
43215
,
A D
XDA
W
DCCABAAC
3.2.2 Junction Tree
Junction Tree
27
Step 1
Step 2
Step 3
Step 4 Join Tree
Step 5 Join Tree Junction Tree
Step
Step 1
3.3 3.4
Step 2
4 2
3.4
3.5
Step 3
1
2
3.5 3.6
Step 4 Join Tree
Join Tree
3.6 2 Join Tree 2 Join Tree
3.7
28
Step 5 Join Tree Junction Tree
Join Tree Junction Tree dom( )
Junction Tree
2 mail box
mail box
message Junction Tree evidence
evidence
3.8 3.9
Join Tree Junction Tree 3.10 i iA
iC i iS i
A
D
F
H
B
I
E
G
C
J
A
D
F
H
B
I
E
G
C
J
A
D
F
H
B
I
E
G
C
J
3.4
A,B,D B,C,E
B,D,E
F,H G,J
E,F,G
D,E,F
D,E
E,F
F,G
B,D B,E
F G
B
F,G,I
D
E
3.6
3.53.3
29
A,B,D B,C,E
B,D,E
F,H G,J
E,F,G
D,E,F
D,E
E,F
F,G
B,D B,E
F G
F,G,I
A,B,D B,C,E
B,D,E
F,H G,J
E,F,G
D,E,F
D,E
E,F
F,G
B,D B,E
F G
F,G,I
3.7 Join Tree
2A 3A
4A 5A 6A
1A321 ,, AAA 321 ,, AAA
42 ,AA 42 ,AA 532 ,, AAA 532 ,, AAA 63, AA 63, AA
2A 3A32 , AA
21 : AS 322 ,: AAS 33 : AS
422 ,: AAC4
422 ,: AAC4
5323 ,,: AAAC5
5323 ,,: AAAC5
634 ,: AAC6
634 ,: AAC6
3211 ,,: AAAC321 ,,
3211 ,,: AAAC321 ,,
3.8 2 3.9 3.8 Join Tree
3.10 Junction Tree
30
3.3.3 Junction Tree
3.10 Junction Tree )( 4AP
evidence E eE evidence
E E eE 1 eE 0
4A 2C
2C i iC
iiC 4C
1C 4 4C }{ 6 1C
1C },,{ 321 AAA 3 1A 2A
3A33
664SA
4
1C 3 mail box 3S
232
5},{
53SAA mail box 2S
1C 2C1
1C
1C },,,,{ 321431
11 1A 3A
)(
),()(),(),()(
),(),()()(),(
)},(),,(),(),(),,({
1 3
1 3
1 3
2
34321
3133432321211
3132121134323
31321211343231
A A
A A
A A
A
AAAAAAAA
AAAAAAAA
AAAAAAAA
1 mail box 1S
2C1
4 4A )( 4AP
)( 4AP
Junction Tree 3.11
2 1 3
2
1 3
2
)}),()(),(),()((),({
})),()(),(),()((),({
}{)(
3133432321211424
3133432321211424
144
A A A
AA A
A
AAAAAAAAAA
AAAAAAAAAA
AP
5 53 6 64
2 1 3 65)}({)( 6532144 A A A AAAP
31
21 : AS 21 : AS 322 ,: AAS 322 ,: AAS 33 : AS 33 : AS
422 ,: AAC4
422 ,: AAC4
5323 ,,: AAAC5
5323 ,,: AAAC5
634 ,: AAC6
634 ,: AAC6
3211 ,,: AAAC321 ,,
3211 ,,: AAAC321 ,,
3
64S2
53S
1
11 S
3.11 )( 4AP Junction Tree
Junction Tree X
Step 1 E eE evidence
Step 2 X xC
Step 3
iC jC
iC iC
i iC jC ijSijS
i
Step 4 xC Step 3 xC
)|( eXP
xC xC
X )|( eXP
3.4 Bayes Net Toolbox
Bayes Net Toolbox
Bayes Net Toolbox MATLAB California Berkley
MATLAB Math Works
Bayes Net Toolbox K2
Junction Tree
K2
32
4
2
CPT
4.1
4.1.1 Dijkstra
2
Dijkstra 2
Dijkstra
1
K o
K o
o ic
1 i K K
33
Dijkstra
Step 1 { j } jc
j 0jF Kj
o o 0oc oi Ko
Step 2 i { m } imim tcc
imim tcc iFm imt i m
Step 3 K }:){min( Kppcc pj jc j
Kj
Step 4 K ji Step2
4.1.2
2
Dijkstra
2 Dijkstra
A B
C
A B
C 2 B
C Dijkstra
4.2 2
2
34
2
4.2.1
2
K2
256
2
3
2.2 – 1
3 30 30
50 50 4.1 4.1 4.7
[ ]
30 30 40 40 4.2
30 40 10
4.1 30 30 50
50
35
4.1 30 30 50 50
4.2 30 30 40 40
5
4.3
4.3
36
2
4.1 5
4.4
4.1
3
4.4
15 15 30 30 3
4.5
37
4.5
148 108 2
3 1 2 1 3
4.6
4.6
2
3
38
4.2
4.2
100
4.7
4.7
39
10
4.3
4.3
[ ]
26
9
2
5 100
35
10
27
6
7 CD
5
4.3 10 A
2 A
4.8
5
6 B
B
4.9
40
4.8 A
4.9 B
4.10 4.10
4.10
41
4.10
2
4.11 4.10
1
2
42
1
2
4.11
4.11 A
2 A
4.12 1 2 1
4 B
B 4.13
43
4.12 A
4.13 B
4.14
1 2
44
4.14
3
(i)
(ii)
(iii)
( ) ( ) ( ) 3
4.15 A B
( )
4.15 ( )
1
2
45
( ) ( ) ( )
4.15
( ) ( ) ( ) 3
A ( ) ( ) 1 ( )
B ( ) ( ) ( ) 1 C
2 2 4.16
4.16
3
60m 88
60m 200m 88 200m 80 3
46
4.16
4.17 4.17
4.17
47
2
2%
0% 4.18
4.17 4.18 100 150 200
50 194 50 170
32 170 30 3
4.18 2 0
20m
2
2
1
2
A 118 138
B 101 155
48
4.2.2
4.2.1 15
7
7 2
5
4.2.3
2
2
2
2
K2
49
4.2.3
4.2.2
5 5
4.2.2
7
5
7
7
7 256
5
120
120
4.4
-1438.6
4.4
4.4 4.19
50
4.19 4.4
4.4
4.4 1 4.2.2
4.2.4
15 256 K2 K2
2 3 12
A
B
A B
12
51
A B
12
4 2
4.5 8
4.5 8
4.5
1 A A A
2 A A B
3 A B A
4 A B B
5 B A A
6 B A B
7 B B A
8 B B B
1
1 K2 4.20
2
52
4.20 1
2
2 K2 4.21
4.20
4.21 2
4.21 2
3
3 K2 4.22
4.20
53
4.22 3
4
4 K2 4.23
4.21
4.23 4
5
5 K2 4.24
4.18
54
4.24 5
6
6 K2 4.25
4.21 4.23
B
4.25 6
7
7 K2 4.26
4.26 4.22
55
4.26 7
8
8 K2 4.27
4.27 8
4.20 4.27 2
56
4.6
4.6 4.6
2 10 6
5 4
3
2
B 7
2
4.2.5 4.2.6
4.6
A B C
1 -3795.9 -3721.4 -3731.3
2 -3873.5 -3804.5 -3814.4
3 -3583.3 -3514.9 -3524.3
4 -3705.4 -3637.0 -3646.3
5 -3671.4 -3594.2 -3605.0
6 -3701.2 -3624.0 -3634.8
7 -3492.5 -3415.3 -3426.1
8 -3502.0 -3424.7 -3435.5
4.2.5 CPT
2 CPT
4.7 CPT 4.7 5
30 30
50
57
4.7 CPT
3030
5050
0.5714 0.3878 0.0408
0.0000 0.8750 0.1250
0.0784 0.9216 0.0000
0.7419 0.2581 0.0000
0.1111 0.8889 0.0000
0.9286 0.0000 0.0714
0.0000 0.6667 0.3333
0.0385 0.5769 0.3846
0.6154 0.1538 0.2308
0.6250 0.3750 0.0000
CPT A CPT
30
58
4.2.1
60m
1
60m 200m
200m
59
60m
200m
4.2.6
evidence 4.2.5
evidence evidence
5
evidence 4.8 4.8
30 30 50 50
30
30 50 50
4.2.1 4.1 30 50
30 50
4.8
60
4.8 evidence
30 30 50 50
0.6332 0.1558 0.2110
0.5315 0.3941 0.0744
evidence 4.9 4.9
4.2.1 4.3
4.9
4.9 evidence
0.1404 0.1235 0.3153 0.2973 0.1235
0.2269 0.1842 0.1121 0.1786 0.2982
evidence 4.10 4.10
4.2.1
4.4
4.10 evidence
0.1975 0.4657 0.2466 0.0902 0.0000
0.0847 0.6110 0.1731 0.1215 0.0097
evidence 4.11
4.11 15 15
30 4.2.1 4.5
15
30 15 15 30
4.5 4.11
61
4.11 evidence
15 15 30 30
0.6060 0.2804 0.1136
0.6488 0.2315 0.1197
evidence 4.12
4.12 3 1
1 2 4.2.1 4.6
4.12
1 4.12
4.12 evidence
3 1 2 1
0.3793 0.2875 0.3332
0.4015 0.2807 0.3178
evidence 4.13
4.2.1
4.7 1
3 5 4.13
4.13 evidence
0.0882 0.9118
0.3943 0.6057
CPT evidence
4.8 4.13
5
K2
2
62
4.3
4.3.1
0 13 146
4.2.1
7
5 32 4
16 146
5
4 4.2.1 4.8
4
4
4.14 4.14
63
4.14
12
8
15
28
14
6
14
2
10
4
13
4
1
10
6
1
4 16
4.15
64
4.15
33
4
20
40
2
3
7
0
23
4
2
4
0
0
4
2
4.28
3
420m 48 710m 52 710m
48
4.28
65
4.3.2
4.2.2
4.2.3
5 120 K2
4.16 4.17
-935.3769 4.16
4.29 4.16
4.30
4.16 4.29
66
4.17 4.30
4.29 4.16
4.30 4.17
4.29 4.30
4.16 1 4.17
67
1
3
4.3.3
4.16 1
3
4.31
3
4.31 4.16
4.17 1
3
4.32
3
68
4.32 4.17
4.31 4.32
4.1.1
4.3.4 CPT
4.31 4.32 CPT 2
CPT
CPT B
69
30
30 50 50
4.31 4.32
4.32 CPT
4.31 4.32 4.31
CPT
3
3
3 1 2
1
1 2 1
1 1
CPT 4.18 4.18 1 16
4.14 5
70
4.18 CPT
1 2 3 4 5 6 7 8
0.0250 0.0250 0.3750 0.0750 0.0250 0.1500 0.0000 0.0250
0.1019 0.0648 0.0000 0.2315 0.1204 0.0000 0.1296 0.0093
9 10 11 12 13 14 15 16
0.1250 0.0750 0.0000 0.0750 0.0250 0.0000 0.0000 0.0000
0.0463 0.0093 0.1204 0.0093 0.0000 0.0926 0.0556 0.0093
4.18 3 6 8 9 10 12
13 4.19 1 2 4 5
7 11 14 15 16 4.20 4.19
4.20
4.19 8 4.20
15 16
4.43
3 0.3750 0.0000
6 0.1500 0.0000
9 0.1250 0.0463
10 0.0750 0.0093
12 0.0750 0.0093
8 0.0250 0.0093
13 0.0250 0.0000
71
4.44
4 0.0750 0.2315
7 0.0000 0.1296
5 0.0250 0.1204
11 0.0000 0.1204
1 0.0250 0.1019
14 0.0000 0.0926
2 0.0250 0.0648
15 0.0000 0.0556
16 0.0000 0.0093
72
5
5.1
2
2
2
3
Bayes Net Toolbox
4 2
2
12
2
73
2
CPT
CPT
CPT
CPT
CPT
CPT
CPT
CPT
CPT
CPT
74
CPT
CPT
CPT
2
evidence
K2
4
2
CPT
CPT
CPT
CPT 30 30
50 50
CPT
CPT 3
75
3
1 2
5.2
2
3
4 4 48
256 5
1
2 10
6 5 4
2
76
77
1 C.M.
-
Jan. 2008
2 Cooper G.F. A Bayesian method for the induction of probabilistic networks from
data Machine Learning Vol.9 pp.309-347 2002
3 Finn V.Jensen Thomas D.Nielson Bayesian Networks and Decision Graphs
Second Edition Springer - Verlag 2007
4 [ ] Mar. 1994
5
Vol.53 12 pp.672-677 2008
6 2006
7
2008
8
Vol.37 3 pp.769-785 2007
9 Bayes Net Toolbox for Matlab
http://bnt.googlecode.com/files/FullBNT-1.0.4.zip 2009 7 5
10 Google Maps http://www.google.co.jp/maps 2010 1 8
11 How to use the Bayes Net Toolbox
http://www.cs.ubc.ca/~murphyk/Software/BNT/usage.html 2009 7 5
78
[1]
2009 12 19
79
A
2
CPT
4.2.5 CPT
CPT 5
A.1 CPT
0.1224 0.7959 0.0000 0.0000 0.0816
0.0000 1.0000 0.0000 0.0000 0.0000
0.0000 0.5882 0.1569 0.2549 0.0000
0.4516 0.3871 0.0968 0.0000 0.0645
0.0000 1.0000 0.0000 0.0000 0.0000
0.2143 0.7857 0.0000 0.0000 0.0000
0.0000 0.1429 0.1429 0.7143 0.0000
0.0000 0.1346 0.0192 0.6923 0.1538
0.4615 0.4615 0.0000 0.0000 0.0769
0.0000 0.8750 0.1250 0.0000 0.0000
A.2 CPT
0.3311 0.0541 0.3446 0.2095 0.0608
0.1296 0.1944 0.4815 0.1204 0.0741
80
A.3 CPT
1515
3030
0.5102 0.3265 0.1633
0.8750 0.1250 0.0000
0.2549 0.5686 0.1765
0.3871 0.1935 0.4194
0.3333 0.5556 0.1111
1.0000 0.0000 0.0000
0.6190 0.2381 0.1429
0.7500 0.0769 0.1731
0.4615 0.5385 0.0000
0.0000 0.7500 0.2500
A.4 CPT
0.5781 0.4219
A.5 CPT
3 1 2 1
15 0.5758 0.2803 0.1439
15 30 0.0633 0.3924 0.5443
30 0.1111 0.0667 0.8222
81
A.6 CPT
0.0000 1.0000
0.1250 0.8750
0.0588 0.9412
0.1290 0.8710
0.3333 0.6667
0.6429 0.3571
0.3810 0.6190
0.3846 0.6154
0.2308 0.7692
0.0000 1.0000
A.7 CPT
0.0366 0.0000 0.3049 0.5488 0.0000 0.1098
0.2500 0.0000 0.0714 0.1429 0.2143 0.3214
0.0842 0.1053 0.2632 0.1684 0.2105 0.1684
0.1373 0.2745 0.0588 0.2157 0.0196 0.2941
A.8 CPT
0.0260 0.0000 0.4156 0.4805 0.0000 0.0779
0.3200 0.0000 0.1200 0.0800 0.2400 0.2400
0.0476 0.1619 0.2571 0.1619 0.2190 0.1524
0.1429 0.2245 0.1020 0.1837 0.0612 0.2857
82
A.9 CPT
0.1111 0.1111 0.3333 0.4444
0.0000 0.3333 0.1111 0.5556
0.0435 0.1304 0.3478 0.4783
0.2857 0.2857 0.1429 0.2857
0.0000 0.3333 0.0000 0.6667
0.3519 0.0556 0.4815 0.1111
0.1500 0.2000 0.5000 0.1500
0.4875 0.0875 0.2875 0.1375
0.3514 0.0811 0.4865 0.0811
0.2857 0.0714 0.3571 0.2857
A.10 CPT
0.9722 0.0278 0.0000 0.0000
0.0000 0.0000 1.0000 0.0000
0.0000 0.0000 1.0000 0.0000 60m
0.0000 0.0000 0.0000 1.0000
0.7692 0.1154 0.0000 0.1154
0.0667 0.2000 0.5333 0.2000
0.0000 0.0800 0.8400 0.0800 60m 200m
0.1818 0.0455 0.0909 0.6818
0.1500 0.2000 0.4000 0.2500
0.2500 0.1667 0.4167 0.1667
0.1538 0.1923 0.1923 0.4615 200m
0.3182 0.1818 0.5000 0.0000
A.11
0.6484 0.3516
83
A.12 CPT
60m60m
200m200m
0.2222 0.3333 0.4444
0.0000 0.3333 0.6667
0.1739 0.3913 0.4348
0.1429 0.7143 0.1429
0.0000 0.6667 0.3333
0.4444 0.2778 0.2778
0.2500 0.3500 0.4000
0.4125 0.3375 0.2500
0.4595 0.3243 0.2162
0.1429 0.3571 0.5000
A.13 CPT
5050
170170
60m 1.0000 0.0000 0.0000
60m 200m 0.9545 0.0455 0.0000
200m 0.8636 0.0909 0.0455
60m 0.8889 0.1111 0.0000
60m 200m 0.6364 0.1818 0.1818
200m 0.5690 0.1379 0.2931
A.14
0.1818 0.8182
0.9343 0.0357
0.1194 0.8806
0.4308 0.5692
0.7187 0.2813
0.2619 0.7381
84
B
CPT
4.3.4
CPT CPT 5
B.1 CPT
30 30 50 50
0.5000 0.4474 0.0526
0.2083 0.5000 0.2917
B.2 CPT
0.2258 0.7419 0.0000 0.0000 0.0323
0.0000 0.3913 0.1739 0.4348 0.0000
0.0000 0.1923 0.1154 0.6346 0.0577
0.4375 0.4688 0.0313 0.0000 0.0625
0.1000 0.7000 0.1000 0.0000 0.1000
B.3 CPT
30 0.3774 0.0189 0.0755 0.4717 0.0566
30 50 0.1286 0.1857 0.5000 0.0857 0.1000
50 0.0800 0.3600 0.5200 0.0400 0.0000
85
B.4 4.31 CPT
15 15 30 30
0.5135 0.3108 0.1757
B.5 4.32 CPT
15 15 30 30
3 0.7885 0.1731 0.0385
1 2 0.5238 0.4048 0.0714
1 0.2407 0.3704 0.3889
B.6 CPT
0.5135 0.4865
B.7 4.31 CPT
3 1 2 1
15 0.5395 0.2895 0.1711
15 30 0.1957 0.3696 0.4348
30 0.0769 0.1154 0.8077
B.8 4.32 CPT
3 1 2 1
0.3514 0.2838 0.3649
86
B.9 CPT
0.2727 0.7273
0.3158 0.6842
0.6667 0.3333
0.6667 0.3333
3
0.7500 0.2500
0.0000 1.0000
0.1818 0.8182
0.0000 1.0000
0.5000 0.5000
1 2
1.0000 0.0000
0.0000 1.0000
0.1304 0.8696
0.1429 0.8571
0.0556 0.9444
1
0.0000 1.0000
B.10 CPT
1 2 3 4 5 6 7 8
0.7095 0.0270 0.0541 0.1284 0.0000 0.0068 0.0135 0.0000
9 10 11 12 13 14 15 16
0.0338 0.0000 0.0135 0.0000 0.0000 0.0000 0.0135 0.0000
B.11 CPT
420 420 710 710m
0.3243 0.3514 0.3243
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