Ignite Notes: “Nobody Told Me There’d Be Bayes Like This”

18 Dec

Above is a link Ignite talk about probability and Bayes’ Rule.

I gave the talk in December 2011 at Ignite Dublin at the Science Gallery, it was the low-point of a brilliant line-up organised by Conor Houghton (his last time organising Ignite Dublin: he will be  greatly missed there).

The full notes are below.

This is a sequel to an Ignite talk I have previously, entitled “Probably Approximately Confused”. Very helpfully, I gave the two talks in different cities; of the couple of hundred people who saw one or the other, only two people saw both live.

The Ignite format is that talks last 5 minutes. You have 20 slides, which auto-advance every 15 seconds. The notes below are more or less exactly what I said during the talk. I have also added a couple of illustrations from my slides.

  1. I’m going to talk for the next few minutes about dangerous animals such as sharks
    • And even more dangerous animals such as cows
    • And Rev Thomas Bayes, who formulated Bayes Theorem in the 1700s
  2. I do research in artificial intelligence & machine learning
    • We use Bayes Rule in understanding medical data
    • Others use it for robot control
    • Almost all spam detection software uses it too
  3. Everyone who works in science, engineering, finance or forecasting needs probability and Bayes Rule if they have data with uncertainty
    • We use Probability to quantify the uncertainty that allows us to make rational decisions
  4. Defining probabilities seems simple
    • You can express how likely it is for something to happen with a number in between 0-1
    • But mistakes are made so commonly by professionals that they end up getting names such as the Prosecutor’s Fallacy
    • I’d like to make to explain to you how to avoid making mistakes like those
  5. One problem we have with probabilities is mis-assigning risk:
    • We are more scared of sharks than cows
    • But about 1 person per year in USA killed by sharks
    • While cattle kill about 20 people/yr in USA [source]
  6. In general, we assign high probability to high-visibility threats but unlikely threats
    • This woman is concerned about jackhammer noise harming her unborn baby [source]
    • But apparently not so concerned about smoking
  7. Of course, she’s not the only parent who makes bad estimates about relative risks
    • What about parents who won’t let kids run in case they fall, walk to school because of near-zero risk of kidnapping or bogeymen, or get MMR vaccines?
  8. So people are naïve about probability. What should we do? Take advantage of them!
    • Here’s my plan: rent out Croke Park football pitch
    • Cover it with a layer of 100 million M&Ms
    • Put a secret mark on the bottom of one
  9. People pay €2 to go in blindfolded with a tweezers
    • If you pick the right one, I’ll give you half the profits
    • Any takers? No? It doesn’t seem like a good deal
  10. And yet millions of people every week buy EuroMillions lottery tickets with worse odds
    • 1 in 116,531,800
    • This example shows that we are better able to appreciate probabilities when presented with hard numbers
  11. Let’s return to the cow and the shark
    • I’m fairly rational: why is it I don’t mind letting my kids into a cow-infested grass, but I wouldn’t let them near shark-infested water?
  12. We can decompose the probabilities:
    • P(death caused by cow) = P(cow causing death) P(meeting cow) / P(death)
    • This is Bayes’ Rule!
  13. Likewise:
    • P(death caused by shark) = P(shark causing death) P(meeting shark) / P(death)
    • This captures our intuition well:
    • Individual sharks are more dangerous than individual cows, but much more rarely encountered by humans
    • So on aggregate cows cause more deaths
  14. Let’s consider the kind of problem that often appears in studies of probability:
    • A randomly chosen person is tested for a disease that affects 1 in 1,000
    • Get positive result from a test
    • The test has 99% accuracy
  15. What do you think?
    • Hands up if you think they probably DON’T have it
    • If you put up your hand,  you are right: let’s figure it out
  16. We saw from the M&Ms example that it’s easier if we use hard numbers: “natural frequencies”:
    • So say we have 100,000 people:
    • 100 will have disease, other 99,900 won’t
  17. The test will give a correct positive result for 99 of the 100 with disease
    • Importantly, the test will give a  false positive for 1% of people: 999
    • It will have a correct negative result for 99%
  18. So we can combine the numbers
    • Of all the people who get a positive result (1098), only 99 actually have cancer: 9%
  19. There have been a lot of research using tests like this with various professionals
    • They conclude that doctors, lawyers and other professionals get these things wrong somewhere between 50% and 90% of the time
  20. So if you were following this,
    • And if you now know to reason in terms of hard numbers when you want to work with probabilities
    • You will be at the upper end of the Bell curve!

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