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In response to Simpson's Paradox
Comment author: Daniel_Burfoot 13 January 2011 04:37:12AM *  3 points [-]

Good post, thanks. One comment:

It may appear that the partitioned data always give a better answer than the segregated data. Unfortunately, this just isn't true.

First, I assume you mean "aggregated", otherwise this statement doesn't make sense.

Second, I don't believe you. I say it's always smarter to use the partitioned data than the aggregate data. If you have a data set that includes the gender of the subject, you're always better off building two models (one for each gender) instead of one big model. Why throw away information?

There is a nugget of truth to your claim, which is that sometimes the partitioning strategy becomes impractical. To see why, consider what happens when you first partition on gender, then on history of heart disease. The number of partitions jumps from two to four, meaning there are fewer data samples in each partition. When you add a couple more variables, you will have more partitions than data samples, meaning that most partitions will be empty.

So you don't always want to do as much partitioning as you plausibly could. Instead, you want to figure out how to combine single partition statistics corresponding to each condition (gender, history,etc) into one large predictive model. This can be attacked with techniques like AdaBoost or MaxEnt.

Comment author: gerg 13 January 2011 05:56:59PM 3 points [-]

Second, I don't believe you. I say it's always smarter to use the partitioned data than the aggregate data. If you have a data set that includes the gender of the subject, you're always better off building two models (one for each gender) instead of one big model. Why throw away information?

If you believe the OP's assertion

Similarly, for just about any given set of data, you can find some partition which reverses the apparent correlation

then it is demonstrably false that your strategy always improves matters. Why do you believe that your strategy is better?

Comment author: gwern 06 January 2011 08:54:28PM *  5 points [-]

If I may, I prefer the fuller version:

"...their judgment was based more upon blind wishing than upon any sound prevision; for it is a habit of mankind to entrust to careless hope what they long for, and to use sovereign reason to thrust aside what they do not fancy."

Also, dupe: http://lesswrong.com/lw/2ev/rationality_quotes_july_2010/28gb?c=1

Comment author: gerg 10 January 2011 10:09:01AM 0 points [-]

Ha - that post refers to Diax's Rake, which is what happened to spur me to find the Thucydides quote in the first place!

In other news, I've invented this incredible device I call a "wheel".

Comment author: gerg 03 January 2011 09:08:12PM 13 points [-]

It is a habit of mankind to entrust to careless hope what they long for, and to use sovereign reason to thrust aside what they do not desire.

-- Thucydides

Comment author: Peter_de_Blanc 03 December 2010 09:45:03PM 1 point [-]

If your beliefs are defeated whenever they clash with reality, then you have attained a mastery of rationality that very few humans achieve. Torvalds' quote looks to me like an "is" statement rather than an "ought" statement, so I can't agree with your interpretation.

Comment author: gerg 09 December 2010 02:48:28AM 0 points [-]

Interesting nuance. You have taken "loses" to mean "defeated", presumably leading to "and therefore updated"; I agree that this is by no means an automatic process. But I took "loses" to mean "is less accurate" (which of course makes my interpretation more tautological).

Comment author: Peter_de_Blanc 03 December 2010 10:48:22AM 6 points [-]

I felt a desire to argue against this quote, but of course a better idea would be to ask what it means.

I'm guessing that "practice" means "the way people are solving this problem now," while "theory" means "the study of what makes a problem-solving method good."

If theorists invent some method that they think is good, but which has already been rejected by practitioners, then I would guess that the theorists have a wrong notion of "good," and they should update their theory on the evidence. If the theorists invent a new method, then there is a chance that it is an improvement, and it may catch on.

Comment author: gerg 03 December 2010 04:21:35PM 6 points [-]

My first reading of this quote was essentially "the map loses to the terrain". I interpreted "theory" as "our beliefs" and "practice" as "reality".

Comment author: Relsqui 10 November 2010 04:49:43AM 1 point [-]

I see what you mean, but I think that would have distracted from the point of the post, which had nothing to do with the fields being used as examples.

Comment author: gerg 12 November 2010 07:57:02AM 0 points [-]

Possibly, yes; but reading a discussion about a topic I don't know anything about is hard, so I'm less likely to get anything out of it, despite the fact that it is there in what you wrote. I'm claiming that the additional "distracting" material would actually serve as a hook to get the reader interested in putting effort into understanding the point of the post.

Comment author: gerg 09 November 2010 01:35:42AM 1 point [-]

This post, which concentrated on people's commentary about a field of inquiry, could have been improved by including some summary of the field being commented on.

In response to comment by gerg on Politics as Charity
Comment author: Wei_Dai 26 September 2010 10:38:22PM 6 points [-]

What is the probability your vote will make a difference? seems to be the state-of-the-art in the "deciding vote" type of reasoning. It concludes "On average, a voter in America had a 1 in 60 million chance of being decisive in the presidential election."

Comment author: gerg 27 September 2010 04:27:10PM *  1 point [-]

I'd need to read it again, with pen and paper, to gain an understanding of why the Student-t distribution is the right thing to compute. At the very least I can say this: the probability of one's vote tilting the election is certainly higher in very close elections (as measured beforehand by polls, say) than in an election such as Obama-McCain 2008. The article you quoted suggests the difference in probabilities is much higher than I anticipated. (Unless my calculation, which models the closest possible election, is incorrect.)

Edited to add: Okay, I've incorporated the probability p that the coin lands heads into the calculation. Even when p=50.05% instead of 50% (closer than any presidential election since Garfield/Hancock), the chance of one vote tilting the election drops by over four orders of magnitude. So for practical purposes, my initial calculation is irrelevant. - At least this was a good lesson in bias: this argument was easy to find, once Wei's comment got me to consider the alternative in the first place.

In response to Politics as Charity
Comment author: gerg 26 September 2010 10:25:53PM *  0 points [-]

Jane estimates the probability of her vote tilting the presidential election at 1 in 1,000,000; Eric estimates the probability of his vote tilting the presidential election at 1 in 100,000,000. I find both of these estimates orders of magnitude too low.

Eric presumably is modeling the election by saying that with 100,000,000 voters (besides himself), there are 100,000,001 outcomes of their votes, only one of which is a tie which his vote will break. But his conclusion that the odds of deciding the election are about 1 in 100,000,000 assumes that all of these outcomes are equally probable, which is a hard-to-defend assumption.

If every other voter is flipping a fair coin to determine their vote, for example, then the probability of a tied vote is exactly 100,000,000! / [ (50,000,000!)^2 * 2^100,000,000], which is approximately 1/12,500. Moreover, I estimate that a solid 40% of the voters will vote Republican no matter what, and a solid 40% will vote Democrat no matter what. If the other 20,000,000 voters flip their fair coins, now the probability of a tied vote is approximately 1/5,600.

This model is oversimplified, of course, because factors that tend to bias individual votes (such as the current economy) will tend to bias many votes in the same direction. Still, I am much more confident in a 1-in-10,000 chance to affect the presidential election outcome than I am in 1-in-100,000,000.

I also agree with Kaj's comment that my vote influences other people to vote, which would make the odds of affecting the outcome better still.

Comment author: TobyBartels 22 August 2010 12:30:01AM 0 points [-]

I agree. But on the other hand I wouldn't worry about it too much. You get the point across to newbies, and veterans already know what you're talking about without the pictures. The only real danger is somebody who has read the rules but has never played games. (But since you linked to a site with the rules, maybe that is a danger after all!)

Comment author: gerg 22 August 2010 02:51:44AM 0 points [-]

Don't worry: I don't know the rules of Go; I went to the site linked; and I could only find a link to a link to a video tutorial, not a list of rules, so I stopped trying.

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