The BIM formula makes use of Bayes theorem. Can anyone please explain:

  • How to read the probability of the form P(R=1|x,q)? Is it P((R=1|x),q) or P(R=1|(x,q))? Does , stand for AND here?
  • How exactly Bayes theorem being applied to expand it?

enter image description here enter image description here enter image description here


It can be read as the probability of R=1, given (x and y) as your second formula. Anything after | stand for the given part.


$P(x | r=1 \wedge q) = \frac{P(x \wedge R=1 \wedge q)}{P(R=1 \wedge q)}$

$P(R=1|q) = \frac{P(R=1 \wedge q)}{P(q)}$

$P(x|q) = \frac{P(x \wedge q)}{p(q)}$


$$P(R=1|x,q) = \frac{P(x | R=1 \wedge q)*P(R=1|q)}{P(x|q)} =$$

$$\frac{P(x \wedge R=1 \wedge q)}{P(R=1 \wedge q)} * \frac{P(R=1 \wedge q)}{P(q)}* \frac{P(q)}{P(x \wedge q)} =$$ $$\frac{P(x \wedge R=1 \wedge q)}{P(x \wedge q)}$$

| improve this answer | |

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.