Bayes’ theorem explained with examples and implications for life.
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I didn’t say it explicitly in the video, but in my view the Bayesian trap is interpreting events that happen repeatedly as events that happen inevitably. They may be inevitable OR they may simply be the outcome of a series of steps, which likely depend on our behaviour. Yet our expectation of a certain outcome often leads us to behave just as we always have which only ensures that outcome. To escape the Bayesian trap, we must be willing to experiment.

Special thanks to Patreon supporters:
Tony Fadell, Jeff Straathof, Donal Botkin, Zach Mueller, Ron Neal, Nathan Hansen, Saeed Alghamdi

Useful references:
The Signal and the Noise, Nate Silver
The Theory That Would Not Die: How Bayes’ Rule Cracked the Enigma Code, Hunted Down Russian Submarines, and Emerged Triumphant from Two Centuries of Controversy, by Sharon Bertsch McGrayne

Bayes’ theorem or rule (there are many different versions of the same concept) has fascinated me for a long time due to its uses both in mathematics and statistics, and to solve real world problems. Bayesian inference has been used to crack the Enigma Code and to filter spam email. Bayes has also been used to locate the wreckage from plane crashes deep beneath the sea.

Music from “Flourishing Views 3”

Comments (39)

  1. It's interesting to note that tests are often, or should be done twice, particularly with rare maladies.

  2. The posterior probability of getting a second positive test for the disease depends on the mechanism of false positives. In a strictly probabilistic sense, your math seems okay unless a person always gets the same result for the test. Imagine testing the group of 1000 people twice (by two different labs or whatever) and the same 11 people end up with positive results. In that case, the probability of actually having the disease given the positive result doesn't change after the second test.

  3. Was this filmed on the South Downs way near Brighton? I love that place! β€οΈπŸ’“πŸ’•

  4. I disagree with Silver that debates between people with 100% and 0% certainty are useless, as long as there is an audience. Debates don't convince people having the debate, they convince the audience. Then there's the example of street epistemology, where you ask for the level of certainty before the conversation. A lot of times, that certainty is reported as 100% before, and lower than 100% afterwards.

  5. What is the probability that this video is actually a good explanation of Bayes Theorem given that it has 2M views? Answer: Lower than you thought.

  6. I might be dumb, but aren't the two tests independent of each other? if one test positive means 9% of true disease (p = 1-9% for test positive and I'm fine), I thought two tests positive and I'm actually fine is (1-9%)*(1-9%)?

  7. The ball & table thought experiment sounds like he was the first person to come up with mine sweeper too! Haha

  8. Amazing video as always, but I do not think the formula was properly applied in order to figure out the probability of actually having the disease as for P(H) you use the probability of having the disease, 0,01,… but that would only be correct if you had been randomly chosen among the population to have the test done on you… but you weren't, you got the test because you had symptoms that match the disease. Or maybe not that specific disease, but if the result comes possitive and you compare the symptoms you have to the symptoms descrived for that disease and they match, then you can no longer use 0.01 as P(H)… I'm no statistician, just a biologist, so if I'm wrong I would love someone to explain it to me why ^^

  9. Well a wise man once said that doing the same thing over and over expecting different results is insanity.

  10. Good analogy. But you also have to consider the certainty of the certainty of the test. How do they know that the test has a 99% certainty? In order to be certain about that, there must be some other way of testing it that is certain in which case you might as well just go and do that other test.

  11. I hope that Juries understand that a 1 in a million odds of a false positive lab test in a case with no other evidence means the person standing trial is statistically more likely to be innocent than guilty.

  12. This theory is freaking awesome! I was on a half-way of understanding something similar about probabilities several years ago when I was in a high school. I'm so glad I get to this video!
    Thanks a lot!

  13. The narcissist has 100% prior, as does the religious fanatic. But many people with prejudices may be amenable to a Bayesian discussion to discover ways to move beyond their prejudices.

  14. this made me think how contradiction does not guarantee mutual exclusion.

    Like in your example: 1) the test is precise 2) we should not fully trust it
    These two ideas may seem contradictory to a casual listener/observer, but as you explained they do not exclude one another. Similarly, if one were to try and argue particle-wave duality to a classic physicist a few centuries ago, they would laugh at you and call you stupid. Nevertheless, it's one of the fundamental ideas on which science is based today. As counter-intuitive as it may seem, the waviness of a thing does not exclude its particle-ness.
    The lesson here is: even if a new "belief" sounds absurd to you, or seems to contradict your knowledge, do not dismiss it. Do not dismiss your prior "belief" in favour of the new information neither. instead. wait. Try to see if the two factoids may be in fact complementary.

  15. Sexist language: the more gender-loaded and more frequent "she" instead of the less gender-loaded and less frequent "he". Bye, bye.

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