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Bayes' Theorem Illustrated (My Way)

(This post is elementary: it introduces a simple method of visualizing Bayesian calculations. In my defense, we've had other elementary posts before, and they've been found useful; plus, I'd really like this to be online somewhere, and it might as well be here.) I'll admit, those Monty-Hall-type problems invariably trip me up. Or at least, they do if I'm not thinking very carefully -- doing quite a bit more work than other people seem to have to do. What's more, people's explanations of how to get the right answer have almost never been satisfactory to me. If I concentrate hard enough, I can usually follow the reasoning, sort of; but I never quite "see it", and nor do I feel equipped to solve similar problems in the future: it's as if the solutions seem to work only in retrospect. Minds work differently, illusion of transparency, and all that. Fortunately, I eventually managed to identify the source of the problem, and I came up a way of thinking about -- visualizing -- such problems that suits my own intuition. Maybe there are others out there like me; this post is for them. I've mentioned before that I like to think in very abstract terms. What this means in practice is that, if there's some simple, general, elegant point to be made, tell it to me right away. Don't start with some messy concrete example and attempt to "work upward", in the hope that difficult-to-grasp abstract concepts will be made more palatable by relating them to "real life". If you do that, I'm liable to get stuck in the trees and not see the forest. Chances are, I won't have much trouble understanding the abstract concepts; "real life", on the other hand... ...well, let's just say I prefer to start at the top and work downward, as a general rule. Tell me how the trees relate to the forest, rather than the other way around. Many people have found Eliezer's Intuitive Explanation of Bayesian Reasoning to be an excellent introduction to Bayes' theorem, and so I don't usually hesitate to

173Jun 3, 2010

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An Agent is a Worldline in Tegmark V

If asked to define what an agent is, my usual answer -- one of them, anyway -- is “a worldline in Tegmark V”. The Tegmark Level V Multiverse (the “V” here is a Roman numeral) is not defined by Max Tegmark (whose hierarchy goes only up to IV), but, as...

Jul 12, 201824

Mathematical Mindset

I agree that optimization amplifies things. I also agree that a mathematical mindset is important for AI alignment. I don't, however, think that a "mathematical mindset" is the same as a "proof mindset". Rather, I think that the latter is closer to being a "programming mindset" -- or, indeed, a...

Jul 11, 201855

Musical setting of the Litany of Tarski

About a year ago, I made a setting of the Litany of Tarski for four-part a cappella (i.e. unaccompanied) chorus. More recently, in the process of experimenting with MuseScore for potential use in explaining musical matters on the internet (it makes online sharing of playback-able scores very easy), the thought...

Mar 23, 201730

Meetup : Washington DC Kennedy Center Meetup with Michael Vassar

Discussion article for the meetup : Washington DC Kennedy Center Meetup with Michael Vassar WHEN: 18 April 2013 12:00:00PM (-0400) WHERE: John F. Kennedy Center for the Performing Arts, 2700 F Street, NW, Washington, DC 20566. (This is very short notice -- 11 hours from posting -- so apologies!) This...

Apr 18, 20134

MIT Challenge complete

Followup to: MIT Challenge: blogger to attempt CS curriculum on own A year after he announced it, productivity blogger Scott Young has successfully completed his "MIT Challenge", an attempt to work through that institution's undergraduate computer science curriculum independently, using the large selection of online material that it has made...

Sep 29, 201230

Daniel Kahneman on Charlie Rose [video]

Daniel Kahneman (of Tversky and Kahneman fame) was interviewed on PBS's Charlie Rose last night, discussing his book Thinking, Fast and Slow (reviewed here by lukeprog): http://www.charlierose.com/view/interview/12185

Feb 29, 20126

Video: Skepticon talks

The talks from Skepticon IV are being posted to YouTube. So far we have: * Richard Carrier on Bayes (my favorite) * Julia Galef on the Straw Vulcan * Greta Christina on angry atheists * Hermant Mehta on math education * David Fitzgerald on Mormonism * J.T. Eberhard on mental...

Nov 26, 201120

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Bayes' Theorem Illustrated (My Way)

The Amanda Knox Test: How an Hour on the Internet Beats a Year in the Courtroom

Mathematical Mindset

Inherited Improbabilities: Transferring the Burden of Proof

komponisto

An Agent is a Worldline in Tegmark V

Mathematical Mindset

Musical setting of the Litany of Tarski

Meetup : Washington DC Kennedy Center Meetup with Michael Vassar

MIT Challenge complete

Daniel Kahneman on Charlie Rose [video]

Video: Skepticon talks

Bayes' Theorem Illustrated (My Way)

The Amanda Knox Test: How an Hour on the Internet Beats a Year in the Courtroom

Mathematical Mindset

Inherited Improbabilities: Transferring the Burden of Proof

An Agent is a Worldline in Tegmark V

Mathematical Mindset

Musical setting of the Litany of Tarski

Meetup : Washington DC Kennedy Center Meetup with Michael Vassar

MIT Challenge complete

Daniel Kahneman on Charlie Rose [video]

Video: Skepticon talks