Bayes' Theorem explained by Yudkowsky | Hacker News Reader

Bayes' Theorem explained by Yudkowsky

yudkowsky.net

57 pointsspydez26 comments

Went back and re-read his tribute to his brother/exhortation to move forward science again. It's like You and Your Research on steroids. If that essay doesn't motivate you, I don't know what will. Insanely brave.

link?

http://yudkowsky.net/other/yehuda

You ought to submit this.

http://news.ycombinator.com/item?id=377412

Has someone figured out a way around the 2nd law of thermodynamics? Or is it not a law anymore? I'm not a physicist, so I don't know these things.

http://www.multivax.com/last_question.html

That's a sci fi story, not hard science.

Absolutely nothing integral to the singularitrons' vision has been demonstrated to any extent. Instead, the opposite is shown by the fact cpu speeds have leveled out.

http://en.wikipedia.org/wiki/Maxwell%27s_demon

http://news.ycombinator.com/item?id=110074

Thanks, those are interesting links. Still, nothing there that seems especially compelling.

Maxwell's demon assumes the energy cost for sorting the molecules is less than the net gain. That looks like another variant of the perpetual motion machine.

The fluctuation theorem says the 2nd law doesn't hold for very, very small entities, but its probability of being correct climbs exponentially as the system scales. So, it is fallacious to then say the 2nd law may not hold at the macro level due to it not holding at the micro level, since the theorem used to support this idea is itself an instance of the idea being false.

Performance hasn't though.

It's always surprising that most people are that bad at math.

.01 x .8 /(.01 x .8 + (.99 x 9.6 / 100)) ~= 0.0776 or 7.8%

Sure, but we expect doctors (who receive much greater education and compensation than most people) to get it right.

What's alarming and interesting isn't that they have a lot of years of school and miss this, but that interpreting diagnostic tests correctly is a core part of their job and they miss it. How many lives are adversely effected and how many billions are wasted by doctors making inappropriate decisions because they don't know how to interpret data correctly?

A few years ago I read that around 50% of all medicine prescribed in the US is providing zero or less net benefit to the patient. Granted by prescribing something doctors get you out of the office and in a few days most things get better on their own. But a lot was simple misunderstanding on the part of doctors about how helpful a given drug actually was.

In case you want to find your source, I'm guessing it was economist Robin Hanson:

http://www.cato-unbound.org/2007/09/10/robin-hanson/cut-medi...

No, it was specifically talking about prescribed medicine. Granted not the cost of said medicine. Something like this (http://www.nytimes.com/2008/10/24/health/24placebo.html) but rather reviewing what drugs patents where taking and comparing it to their symptoms.

Around 15% got it right, which is quite consistent with Sturgeon's Law:

http://en.wikipedia.org/wiki/Sturgeon_law

And in particular with probability. It's amazing how difficult it is for people to fake random data.

If you ask half a class to actually perform and record 100 coin flips and half to fake the data, it's almost trivial to guess which is which either by looking for a string of 5-6 heads or tails in a row (which humans almost never have), or by calculating the percentage flips following a heads that are tails (which should be ~50%, but for humans tends to be much higher).

This is my favorite writing by Yudkowsky: http://www.overcomingbias.com/2008/05/faster-than-ein.html

It bugs me a little that he starts using the phrase "prior probability" before defining it. If your vocabulary already included the word "priors", you probably wouldn't need a Bayes tutorial. :)

[java applet] [java applet] [java applet] [java applet] [java applet]

Which is not to say you shouldn't click! In fact these are the most useful Java applets I've ever seen. He still should've done them with Flash, though.

Do significant digits matter in these sort of probability calculations?

Secondly, do we want doctors to tell us the probablility estimate that we have cancer or do we want doctors to tell us Yes or No?

Personally, I don't care what my probability score is if the answer is "No". Even if the answer was "Yes", an optimistic person would ignore the odds anyway.

Yes, I want the probability estimate, because I want the best information available in that sort of situation. And the word for someone who ignores the odds is not "optimistic" but "foolish", unless the answer makes no difference to your behaviour. (Which is pretty unlikely in the case of cancer.)

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