Author Topic: Week 5: Chapter 8 - Less and Less and Less Wrong  (Read 2017 times)  

Offline Eltanin Publishing

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Week 5: Chapter 8 - Less and Less and Less Wrong
« on: December 10, 2012, 08:24:33 am »
I'm still working on chapter 9 (the chess chapter), and also the chapters are quite different, so I decided to split the week into two threads. If someone has finished chapter 9 and wants to start a thread on it, go right ahead. Otherwise I'll start it in a day or so.

The story about bettor Bob Voulgaris was interesting. I did know that bettors often make many bets, not just one, because they can't be absolutely sure that any one bet will pay off. But if they have a decent system, and make many bets, overall they should make money. Just as a weather forecast's "70% chance of rain" will not mean it rains every time, but over the long haul it will rain 70% of the times that that forecast is made (if it's accurate). Betting is an interesting example, because unlike predicting the weather, where you only have to predict what will happen, the odds are affected by what other people think will happen.

I had heard of the phrase "hedging you bets" but this chapter really helped explain that. I was surprised that Voulgaris could make money no matter what if he had been able to place another bet. That only works because the 2nd bet would have been made at a later time than the first bet, and the odds had changed. You can't place two bets, one on each of two teams in a game, at the same time, and make money no matter what - the odds would cancel each other out (actually I believe you'd lose money every time because the bookie takes a cut). But if you place a bet, and then wait for the odds to change, you might be able to place another bet that will cause you to win money no matter what.

The thing that sticks in my mind the most from this chapter is the idea that people often put too much value in new, recently acquired info - "Usually, however, we focus on the newest or most immediately available information, and the bigger picture gets lost." (approx. loc 4006). The Lakers did poorly for their first few games, and it caused people to think they were terrible and wouldn't do well for the whole season - ignoring long-standing other evidence such as how they were doing the previous year.

I found Bayes's Theorem to be fascinating, and I'm shocked that I never learned about it (or at least, I don't remember it) in various college math and stats classes. I do see Fisher's concern that it requires us to know or estimate the chance of something happening before we got the new info - sometimes this is known, other times we have to estimate. But Bayes's Theorem does a much better job than the standard significance test of 95% (and why 95%? Why not 90%, or 98%?) in determining whether a perceived pattern is due to an actual correlation, or is just a chance occurrence in the huge quantity of data we look through (such as an apparent correlation between which conference wins a football game and who wins a political race). Bayes's Theorem forces you to look at the rationality of your conjecture - how likely is it, really, that a football game influences an election? If a medical test comes back positive, how likely is it, really, that the person has that disease? Frequentists, like Fisher, felt that if you just sampled enough data, the answer would be clear and correct. But I don't care how many times a football game correctly predicted an election - it's not rational, and before given any data (showing the correlation), we'd say that it's very unlikely that the games could influence or predict the election.

"These [frequentist] methods discourage the researcher from considering the underlying context or plausibility of his hypothesis, something that the Bayesian method demands in the form of a prior probability." (loc. ~4106)

I also liked: "We can perhaps never know the truth with 100 percent certainty, but making correct predictions [making predictions that then turn out to be correct/true] is the way to tell if we're getting closer." (~loc 4142)

Silver points out (around loc. 4200) that Bayesian logic can explain why someone's opinions are so resistant to change - if someone's priors are nearly 0 or 100%, the formula shows they won't change much regardless of new information. I also want to point out one thing that was in a footnote that people might not have clicked on to read. At approx. location 4210, Silver says, "I'm not here to tell you whether there are things you should believe with absolute and unequivocal certainty or not...*" and the asterisk takes you to, "Although bear in mind that one of the conclusions of this book is that people are overconfident; we probably have too many beliefs that tend toward the 0 percent or 100 percent end of the spectrum."
 

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    Offline Ann in Arlington

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    Re: Week 5: Chapter 8 - Less and Less and Less Wrong
    « Reply #1 on: December 10, 2012, 10:22:04 am »
    I saw some of the comments in this chapter as relevant to his discussion of pundits as well. . . many of them would assign near 0 or 100 their prior beliefs -- kind of explains Karl Rove's unwillingness to believe it when Fox News called Ohio for the President on election night.  He just wouldn't move his probability of the President winning the election off 0%.

    I also was thinking about this when reading the news about the Nationals having acquired pitcher Dan Haren.  He didn't have a great year last year, some injury issues, which made him not particularly attractive to a lot of teams.  But the Nats looked at his whole career and decided he was worth signing -- they feel like the health issues are past and his history is good.
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