0
$\begingroup$

I'm reading through a lesson on Bayes theorem and I saw this slide: enter image description here

How can model & data be == (data | model) x P(model)?

Does the & not imply multiplication? Otherwise it implies that data == data | model.

| cite | improve this question | | | | |
$\endgroup$
  • $\begingroup$ Here $(A|B)$ means event A happens conditional on the event B happens. $(A \& B)$ means both event $A$ and $B$ happen. $\endgroup$ – user158565 May 25 '17 at 5:20
3
$\begingroup$

Both equations are correct. First one is the definition of conditional probability in terms of joint probability

$ P(Y = y \mid X = x) = \frac{P(X=x\ \,\cap\, Y=y)}{P(X=x)} $

What is incorrect, is calling it Bayes theorem, since it is just the definition of conditional probability.

The & sign is not multiplication, since in mathematics we do not use "&" to denote multiplication. It is what it is, it means probability of observing $X=x$ and $Y=y$ together. It leads to multiplication only when $X$ and $Y$ are independent.

| cite | improve this answer | | | | |
$\endgroup$
  • $\begingroup$ Minor quibble. It still doesn't mean multiplication, even when X and Y are independent (it still means and). It just results in multiplication algorithmically when the probability of the conjunction event is calculated in case the events are independent. $\endgroup$ – Matthew Drury May 26 '17 at 4:59
  • $\begingroup$ @MatthewDurdy good point, I changed the wording. $\endgroup$ – Tim May 26 '17 at 5:23

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.