Figure 3. Age representation, Depression and the probability of Activities.
For our exercise using the Bayesian methodology in Figure 4, it shows how the nodes represented and their specifications would be, since that is the part that interests us.
 |
| Figure 4. Representation of nodes A, B, C with their respective labels |
P(A)
= 0.78
|
P
(C|A, B) = 0.65
|
P
(C|A, ¬B) = 0.86
|
P(B)
= 0.70
|
P
(C|¬A, B) = 0.57
|
P
(C|¬A, ¬B) = 0.75
|
Table 1. Representation of the probability values of each node
To take into account the symbol (Not sing) ¬ represents the event that did not happen.
P (B|C, A)
Exercise 1 Bayesian Probability
We apply the Bayes theorem:
We apply the multiplicative rule theorem to be able to clear P (B, A) and P (C, A) since we do not have these values:
We substitute these terms and simplify:
We apply the total probability rule, since we do not have the probability that is indicated in the denominator. In the case of the numerator we must observe that event B does not depend on event A, as can be seen in the network, they are independent events:
We substitute in the equation and as we observe we already have all the values to be able to calculate the requested value:
However, we must again observe that B does not depend on event A:
Finally we substitute the values and proceed to perform the calculation (remember that if P (B) = 0.70 then P (¬B) = 1-0.70 = 0.30:
 |
We substitute in the equation and as we observe we already have all the values to be able to calculate the requested value:
