Suppose that we have a network like the one in figure
in which we know all the conditional probabilities $P(A_i | B_j)$.
Is it possible to compute the two conditional probability $P(B1 | B2)$ and $P(B2 | B1)$?
How?
Thank you in advance.
Suppose that we have a network like the one in figure
in which we know all the conditional probabilities $P(A_i | B_j)$.
Is it possible to compute the two conditional probability $P(B1 | B2)$ and $P(B2 | B1)$?
How?
Thank you in advance.
From the definition of conditional probabilities: $ P(B_2|B_1) = \frac{P(B_2 \cap B_1)}{P(B_1)} $ Given whether $A_1$ and $A_2$ are true, $B_1$ and $B_2$ become independant events, so that we can write $ = \frac{\sum_c P(B_2|c)P(B_1|c)}{\sum_c P(B_1|c)} $ where the sum is over all possible combinations of $(A_1,A_2)$, $(A_1,!A_2)$...
As all $P(B_i|(!)A_1,(!)A_2)$ are known, this can be calculated.