Bateria_ok bloco_Leve

luz_acessa - G braço_Move

P(B)

0.95

P(L)

0.70

P(G)

0.95

B

T

F 0.10

B, L

T T

T F

F T

F F

P(M)

0.90

0.05

0.00

0.00

X último a disparar

P(X)

[0.8, 0.1, 0.1]

P(Y|X)

0.8 0.1 0.10.1 0.8 0.10.1 0.1 0.8

Y último a tocar

Z impressões dig

P(Z|Y)

1 0 00 1 00 0 1

(X) = P(X)(Y) = (X).P(Y|X) = [0.8 0.1 0.1].P(Y|X) = [0.66 0.17 0.17] (Z) = (Y).P(Z|Y) = [0.66 0.17 0.17].P(Z|Y) = [0.66 0.17 0.17]

Evidencia E+

P(X|E+) = (X) = [0.8 0.1 0.1]P(Y|E+) = (Y).(Y) = [0.66 0.17 0.17] P(Z|E+) = (Z).(Z) = [0.66 0.17 0.17]

X último a disparar

P(X)

[0.8, 0.1, 0.1]

P(Y|X)

0.8 0.1 0.10.1 0.8 0.10.1 0.1 0.8

Y último a tocar

Z impressões dig

P(Z|Y)

1 0 00 1 00 0 1

(Y) = .P(Z|Y).(Z) = .P(Z|Y). [0.8 0.6 0.5]T = [0.8 0.6 0.5]T (X) = .P(Y|X).(Y) = .P(Y|X). [0.8 0.6 0.5]T = [0.75 0.61 0.54]T

Evidencia E-

(Z) = P(E-|Z) = [0.8 0.6 0.5]T

P(X|E+E-) = (X).(X) = (X). [0.8 0.1 0.1] = [0.84 0.08 0.076]P(Y| E+E-) = (Y).(Y) = (Y).[0.66 0.17 0.17] = [0.738 0.143 0.119]P(Z| E+E-) = (Z).(Z) = [0.738 0.143 0.119]

X último a disparar

P(X)

[0.8, 0.1, 0.1]

P(Y|X)

0.8 0.1 0.10.1 0.8 0.10.1 0.1 0.8

Y último a tocar

Z impressões dig

P(Z|Y)

1 0 00 1 00 0 1

(Y) = (X).P(Y|X) = [0.28 0.36 0.36].P(Y|X) = [0.3 0.35 0.35] (Z) = (Y).P(Z|Y) = [0.3 0.35 0.35].P(Z|Y) = [0.3 0.35 0.35]

Nova evidencia E+

(X) = [0.28 0.36 0.36]

P(X|E+E-) = (X).(X) = [0.33 0.352 0.311]P(Y| E+E-) = (Y).(Y) = [0.384 0.336 0.28]P(Z| E+E-) = (Z).(Z) = [0.384 0.336 0.28]

Alarme

João

Terramoto

Maria

RouboP(A)

[0.001 0.999]

P(M|A)

[0.70 0.30]

A

T

F [0.01 0.99]

P(T)

[0.002 0.998]

R,T

T T

T F

F T

F F

P(A|R,T)

[0.95 0.05]

[0.94 0.06]

[0.001 0.999]

[0.29 0.71]

P(J|A)

[0.90 0.10]

A

T

F [0.05 0.95]

A(R) = [0.001 0.999] A(T) = [0.002 0.998] (A) = A(R).P(A|R) + A(T).P(A|T) = A(R).T(P(A|R,T).P(T)) + L(T).P(A|T) = = [0.005 1.995]

P(A|E+E-) = (A).(A) = [0.005 1.995] = [0.0025 0.9975]

J(A) = .P(A|E+E-)/J(A) = .[0.005 1.995] = [0.0025 0.9975](J) = J(A).P(J|A) = [0.0052 0.9948] = P(J| E+E-)

De forma semelhante:(M) = M(A).P(M|A) = [0.01 0.99] = P(M| E+E-)

X

U1Un

Y1Yn

…

…

Dados: X(Ui) , Yi(X) e P(X|U1,…,Un)

Calcular: (X) = i Yi(X)

(X) = Ui X(Ui).P(X|Ui) = Ui P(X|U) i X(Ui).

P(X|E+,E-) = .(X).(X)

Propagar:X(Ui) = X i(X).(UkUi) P(X|U1,…,Un). (ki) X(Uk)

Yj(X) = P(X|E+,E-) / Yj(X)