= 27d567bc2d48d9f40e9ccc20ea370b15)
Kaj_Sotala comments on Open Thread: February 2010 - Less Wrong
You are viewing a comment permalink. View the original post to see all comments and the full post content.
= 783df68a0f980790206b9ea87794c5b6)
Loading…= b715d02e85f7b3b4ae65ca3d3e450868)
Subscribe to RSS Feed
Powered by Reddit
= f037147d6e6c911a85753b9abdedda8d)
You are viewing a comment permalink. View the original post to see all comments and the full post content.
Comments (738)
Bleg for assistance:
I’ve been intermittently discussing Bayes’ Theorem with the uninitiated for years, with uneven results. Typically, I’ll give the classic problem:
3,000 people in the US have Sudden Death Syndrome. I have a test that is 99% accurate; that is, it will wrong on any given person one percent of the time. Steve tests positive for SDS. What is the chance that he has it?
Afterwards, I explain the answer by comparing the false positives to the true positives. And, then I see the Bayes’ Theorem Look, which conveys to me this: "I know Mayne’s good with numbers, and I’m not, so I suppose he’s probably right. Still, this whole thing is some sort of impractical number magic." Then they nod politely and change the subject, and I save the use of Bayes’ Theorem as a means of solving disagreements for another day.
So this leads to my giving a very short presentation on the Prosecutor’s Fallacy next week. The basics of the fallacy are if you’ve got a one-in-3 million DNA match on a suspect, that doesn’t mean it’s three million-to-one that you’ve got that dude’s DNA. I need to present it to bright, interested people who will go straight to brain freeze if I display any equations at all. This isn’t frequentists-vs.-Bayesians; this is just a simple application of Bayes’ Theorem. (I suspect this will be easier to understand than the medical problem.)
I’ve read Bayesian explanations, but I’m aiming at people who are actively uninterested in learning math, and if I can get them to understand only the Prosecutor’s Fallacy, I’ll call Win. A larger understanding of the underlying structure would be a bigger win. Anyone done something like this before with success (or failure of either educational or entertainment value?)
For this specific case, you could try asking the analogous question with a higher probability value. E.g. "if you’ve got a one-in-two DNA match on a suspect, does that mean it’s one-in-two that you’ve got that dude’s DNA?". Maybe you can have some graphic that's meant to represent a several million people, with half of the folks colored as positive matches. When they say "no, it's not one-in-two", you can work your way up to the three million case by showing pictures displaying what the estimated amount of hits would be for a 1 to 3, 1 to 5, 1 to 10, 1 to 100, 1 to 1000 etc. case.
In general, try to use examples that are familiar from everyday life (and thus don't feel like math). For the Bayes' theorem introduction, you could try "a man comes to a doctor complaining about a headache. The doctor knows that both the flu and brain cancer can cause headaches. If you knew nothing else about the case, which one would you think was more likely?" Then, after they've (hopefully) said that the man is more likely to be suffering of a flu, you can mention that brain cancer is much more likely to cause a headache than a flu is, but because flu is so much more common, their answer was nevertheless the correct one.
Other good examples:
Most car accidents occur close to people's homes, not because it's more dangerous close to home, but because people spend most of their driving time close to their homes.
Most pedestrians who get hit by cars get hit at crosswalks, not because it's more dangerous at a crosswalk, but because most people cross at crosswalks.
Most women who get raped get raped by people they know, not because strangers are less dangerous than people they know, but because they spend more time around people they know.