Bayes Net Calculation¶
Given Tables¶
P(LD=T | Cough=T) = P(Cough=T |LD=T) *P(LD)
---------------------------
P(Cough)
= (0.80 * 0.30 + 0.75 * 0.70) * P(LD)
------------------------------------
P(Cough)
= (0.80 * 0.30 + 0.75 * 0.70) * (0.10)
------------------------------------
P(Cough)
= (0.80 * 0.30 + 0.75 * 0.70) * (0.10)
---------------------------------------
(0.80 * 0.30 * 0.10) + (0.30 * 0.30 * 0.90) + (0.75 * 0.70 * 0.10) + (0.05 * 0.70 * 0.90)
= 0.0765
-------
0.189
= 0.40476190476190477
Question
\[P(LD=T|Cough=T,Fever=T)\]
// Bayesian
P(LD=T|Cough=T,Fever=T) = P(Cough=T, Fever=T | LD=T) * P(LD=T)
= Sum(cold) [P(Cough=T,Fever=T| LD=T,cold) * P(cold) * P(LD=T) ] // Skipped a step = that was the mistake
= Sum(cold) [P(Cough=T| LD=T,cold) * P(Fever=T| LD=T, cold) * P(cold) * P(LD=T) ]
= P(LD=T) * Sum(cold) [P(Cough=T| LD=T,cold) * P(Fever=T| cold) * P(cold)]
= P(LD=T) * [P(Co=T|LD=T,C=T) * P(F=T|C=T) * P(C=T) + P(Co=T|LD=T,C=F) * P(F=T|C=F) * P(C=F)]
= 0.10 * ((0.80 * 0.65 * 0.30) + (0.75 * 0.25 * 0.70))
= 0.028725
= P(Cough=T, Fever=T | LD=F) * P(LD=F)
= P(LD=F) * Sum(cold) [P(Cough=T| LD=F,cold) * P(Fever=T| cold) * P(cold)]
= P(LD=F) * [P(Co=T|LD=F,C=T) * P(F=T|C=T) * P(C=T) + P(Co=T|LD=F,C=F) * P(F=T|C=F) * P(C=F)]
= 0.90 * ((0.30 * 0.65 * 0.30) + (0.05 * 0.25 * 0.70))
= 0.060524999999999995
= 0.32184873949579834