Probability Trees

Probability trees, conditional probability, Bayes' Theorem. Best viewed in full screen.

[quicktripgas]

Mind Blown! This is the best explanation of Bayes Therom I have ever seen.

[raveeshmalhotra]

Great Video. Loved it. Understood it. Appreciate it. Thanks

[maryglantz]

This was really helpful, especially in explaining the theorem with a concrete example! Thank you!

[danipan]

Super helpful, thank you so much for the clear explanation! :D

[swarnalihait]

Thank you Ma'm, it was very helpful..

[raghuvirj]

Here is the story format - for those who enjoy story: Note that the values I have used are different than one in this video.

When I saw the formula P(D|+) = P(+|D) * P(D) / ( P(+|D) * P(D) + P(+|~D) * P(~D) ) I was very confused. So I am breaking it down in layman's term below. comment and it up if you find it helpful.

We want to calculate probability of a random person from the population of 1M people - 1, 000, 000 - having HIV when test comes +.

We know that .001 is prevalence so only 1000 people have HIV.

We know that sensitivity or + result when the person has HIV is 99.7%. So out of 1000 people 997 people would test + and 3 would test -.

We know that specificity or - test when person doesn't have HIV is 98.5%. Meaning that out of all people who don't have HIV, 1.5% will still test +. So out of 1M - 1000 = 999, 000 people who don't have HIV, probably staggering 14, 985 people would test + even when they don't have HIV.

So in our population, in total, probably 997+ 14, 985 = 15, 982 people will test positive. Yet, the people with HIV would be probably only 997 out of them.

This means that chance of a person having HIV (997) out of all that tested positive (15, 982) comes to 997/15, 982 or 6.23%.

So bottomline is that our result comes so low because, we are testing random people from the population and very tiny fraction of the population has HIV so we end up testing non HIV people most of the times and therefore our false positives are way to high. So it doesn't help to do testing on random population. We should rather test the population subset like all people who had intercourse with multiple partners and didn't use a condom. Then all the numbers will change and we will get somewhere with our tests.

This is exactly the outcome of the formula:

P(D|+) = P(+|D) * P(D) / ( P(+|D) * P(D) + P(+|~D) * P(~D) )

OR

People

OR

P(D|+) = .997 * .001 / (.997 * .001) + (1-.985) * (1-.001)= 0.000997 / (0.000997 + (0.015*0.999) )= 0.000997 / (0.000997 + 0.014985 )= 0.06238268 = 6.23%

[raghuvirj]

The video is amazing and if you used VAN diagram it would be even more easier!!!! I have used the story format below