Bayes' Theorem (with Example!)

If I get 9% of chance by having the disease given that I tested positive, does it mean that taking other test I have to update P(B) from 0.001 to 0.09?

So It would be:

P(B|A) = [(0.99)*(0.09)]/[(0.99)*(0.09) + (0.01)*(0.91)] = 90.7%

Really enjoying the lecture series - thank you so much for taking the time, I'm learning a lot.

Just a small point relating to binary classification terminology, which I think is confusing on the best of days. In your notation: P( + |D) = probability of testing positive if disease is present (ie, the test sensitivity). Then P( + |ND) = 1 - specificity, where test specificity = P( - |ND), or the probability of testing negative if you don't have the disease.

Accuracy, as I understand, is commonly defined as the total proportion of correct tests divided by all tests (ie true pos + true neg / (all outcomes)), but here you equate it with sensitivity, and then imply that P(+ |ND) = 1 - P(+ | D). (Which is this particular case it may be! - if P(+|D) = P(-|ND)).

Thanks again for the great content.

Thanks a lot professor for this very useful series.
I have question , is correct to have: P(+|disease absent)=1-p(+|disease present) ?

A real Master class on Bayes' (really Bayes-Laplace) Theorem. The best comprehensive treatment of the concept. Wow!

For those of you taking this course; Is there a textbook that you're supposed to use with it?

Amazing explanation of this concept.

perfect

outstanding presentation. Too bad this didn't exist at the start of the semester (finals are a week away).

That is belief calculus, not probably. You are calculating the strength of a belief given complete (100%) "belief" in the probabilities.
What prob and stat fails to do is calculate the strength of the underlying belief, and assumes that strength is 100% certain.
The truth is that, if there is cause and effect, the probabilities are meaningless, and the cause exists, or it doesn't.

I have a bit of an issue with your coin example because those are all independent tests... Otherwise great video, thanks!

Thank you for the informed video. I have one point, it may be obvious to you but it’s not obvious to someone who is new to stats.

The most clear and accessible explanation of Bayes! Thanks

I dont understand sir what game is being played in my life

Awesome explanation

Cancer!? How about A -you've won the Lottery or B you have spent your money for nothing and you have not won the Lottery? I don't really care for the C word! No offense -there are some people waiting on test results! P.S., I love your lectures!