Re: Why Bayes' Rule is useful

Expand Messages
• ... This is the definition of Conditional Probability. ... Bayes Rule is derived from the definition of conditional probability. Hence, all assumptions made
Message 1 of 3 , Jan 31, 2011
> P(H|E) = P(H and E) / P(E)
This is the definition of Conditional Probability.

> P(H|E) = (P(E|H)*P(H))/P(E)
Bayes' Rule is derived from the definition of conditional probability.
Hence, all assumptions made in the definition of conditional probability
will be true even for Bayes' Rule

> Is it because the former requires P(H and E) assumes independence,
P(H and E) does not assume independence (or dependence for that matter).
It just represents joint distribution.

> Why is the definition of conditional probability not as useful as the
Bayes' Rule?
That is because in most applications, when you want to predict P(H|E),
the most estimable quantity that you have with you is P(E|H). For
example, if you want to predict what disease is afflicting a person
based on his symptoms i.e P(Disease | Symptoms), the data that you will
have with you is which diseases have what all symptoms, from which you
can estimate P(Symptoms | Disease).

Regards.

--- In aima-talk@yahoogroups.com, "Jim Davies" <jim.davies@...> wrote:
>
> P(H|E) = P(H and E) / P(E)
>
> is not as useful as Bayes' Rule
>
> P(H|E) = (P(E|H)*P(H))/P(E)
>
> But I'm not sure why. Is it because the former requires P(H and E)
assumes independence, which we might not have?
>
> JimDavies
>
• A good way to memorize Bayes rule is this: P(A,B) = P(A|B)P(B) = P(B|A)P(A) ^ probability of A and B This is always true. You can easily get Bayes rule
Message 2 of 3 , Mar 7, 2011
A good way to memorize Bayes rule is this:

P(A,B)  = P(A|B)P(B)    = P(B|A)P(A)
^ probability of "A and B"

This is always true.

You can easily get Bayes rule by moving one factor under the other side.

Bayes rule allows one to calculate "B given A" when we are given "A given B", ie, it allows to reverse the direction of a conditional probability.

KY
Your message has been successfully submitted and would be delivered to recipients shortly.