MrHen and I are meeting at 8:15 p.m. Central for our first IRC Less Wrong study-group session. Please join us—we will meet here a few minutes before the meeting.
I’ll send out regular announcements closer to the session if there is no recent comment activity here. Please announce if you are planning to attend—it will encourage others to attend too.
Super easy specifics on how to get where we will be: Click on this link and enter a nickname (hopefully something similar to your name here). And that should do it.
All are welcome and you can just lurk if you want. I am there now while I munch on some beans for dinner but the discussion should begin in about an hour.
In the post, How Much Evidence Does It Take, Eliezer described the concept of ‘bits’ of information. For example, if you wanted to choose winning lottery numbers with a higher probability, you could have a box that beeps for the correct lottery number with 100% probability and only beeps for an incorrect number with 25% probability. Then the application of this box would represent 2 bits of information—because it winnows your possible winning set by a factor of 4.
During the chat, we discussed this definition of “bits”. MrHen brought in some mathematics to discuss the case where the box beeps with less than 100% probability for the correct number (reduced box sensitivity, with possibly the same specificity), and how this would affect the calculation of bits.
An interesting piece of trivia came up. Measuring information “base 2” is arbitrary of course and instead of measuring bits we could measure “bels” or “bans” (base 10).
Wow, I wish I’d been there for that (had to go to a trade group meeting) -- that’s one of the topics that interests me!
Btw, I think you mean that a beep-for-incorrect gives you 2 bits of information. Just applying the box will usually (~75% of the time) not indicate either way. The average information gained from an application of the box (aka entropy of the box variable aka expected surprisal of using the box aka average information gain on using the box) would be ~0.5 bits.
How much evidence does it take for you to accept 3:2 odds that your team will win the match given your prior understanding of each team’s performance at various stages of a game?
So I actually have this idea of doing a series (or just a couple) of top level posts about rationality and basketball (or sports in general). I’m partly holding off because I’m worried that the rationality aspects are too basic and obvious and no one else will care about the basketball parts.
But sports are great for talking about rationality because there is never an ambiguity about the results of our predictions and because there are just bucket-loads of data to work with. On the other hand, a surprising about of irrationality can be still be found even in professional leagues where being wrong means losing money.
Anyway, to answer your question: You get two kinds of information from play at the beginning of the game: First, you get information about what the final score will be from the points that have been scored already. So if my team is up 10 points the other team needs to score 11 more points over the remainder of the game in order to win. The less time remaining in the game the more significant this gets. The other kind of information is information about how the teams are playing that day. But if a team is playing significantly better or worse than you would have predicted coming in, their performance is most likely just noise. Regression to the mean is what should be expected. So my prediction of a team’s performance for the remainder of some game is going to be dominated by my priors (which hopefully are pretty sophisticated and based on a lot of data, for college basketball I start here and then adjust for a couple things that can’t be taken into account by that model (the way individual players match up against each other, injuries, any information about the teams’ mental states, etc.)
If you have all this information you can actually give, at any point during a game, the odds for you winning (there are a couple other factors that need to be considered as well, in particular you need to estimate how many possessions there will be in the rest of the game because the information we have about team performance is per/possession not per minute). I’ve also ignored fan attendance in this comment but that is really important evidence as well. I ended up attending the game in person and when I arrived I realized the venue included at least as many fans of the other team as there were fans of my team—and right there the probability my team was going to win dropped by 10%.
Cool. Does IRC work for you? I think I still have a client lurking about somewhere...
And I vaguely remember there being an LW channel at one point. Yep: #lesswrong. And there is a nifty web link in the wiki link. Cool.
EDIT: Yeah, I was wondering about the hhhhhhhhf1. I would have guessed a cat.
Countdown: 13 hours
IRC Meeting At Less Wrong:
MrHen and I are meeting at 8:15 p.m. Central for our first IRC Less Wrong study-group session. Please join us—we will meet here a few minutes before the meeting.
Our topic today is evidence; to discuss the post, How Much Evidence Does it Take? and possibly supporting posts, What is evidence?. Our goal is to build a foundation for discussing Occam’s Razor and Einstein’s Arrogance.
I’ll send out regular announcements closer to the session if there is no recent comment activity here. Please announce if you are planning to attend—it will encourage others to attend too.
Super easy specifics on how to get where we will be: Click on this link and enter a nickname (hopefully something similar to your name here). And that should do it.
All are welcome and you can just lurk if you want. I am there now while I munch on some beans for dinner but the discussion should begin in about an hour.
We’re about to begin our IRC meeting if anyone else wants to join us!
So I ended up at the game in person. How did this go? Any insights to share with those of us who weren’t there?
This is a transcript of the chat log.
In the post, How Much Evidence Does It Take, Eliezer described the concept of ‘bits’ of information. For example, if you wanted to choose winning lottery numbers with a higher probability, you could have a box that beeps for the correct lottery number with 100% probability and only beeps for an incorrect number with 25% probability. Then the application of this box would represent 2 bits of information—because it winnows your possible winning set by a factor of 4.
During the chat, we discussed this definition of “bits”. MrHen brought in some mathematics to discuss the case where the box beeps with less than 100% probability for the correct number (reduced box sensitivity, with possibly the same specificity), and how this would affect the calculation of bits.
An interesting piece of trivia came up. Measuring information “base 2” is arbitrary of course and instead of measuring bits we could measure “bels” or “bans” (base 10).
Wow, I wish I’d been there for that (had to go to a trade group meeting) -- that’s one of the topics that interests me!
Btw, I think you mean that a beep-for-incorrect gives you 2 bits of information. Just applying the box will usually (~75% of the time) not indicate either way. The average information gained from an application of the box (aka entropy of the box variable aka expected surprisal of using the box aka average information gain on using the box) would be ~0.5 bits.
And yes there’s also nats (base e).
I believe the point was that a beep constitutes 2 bits of evidence for the hypothesis that the number is winning.
Countdown: 3 hours till our IRC meeting.
You’re welcome to join us.
How does one access it? Link?
MrHen left these convenient instructions.
I plan to attend.
If I’m home I’ll log in. But I’m going to be watching basketball at the same time so my participation might not be heavy.
How much evidence does it take for you to accept 3:2 odds that your team will win the match given your prior understanding of each team’s performance at various stages of a game?
So I actually have this idea of doing a series (or just a couple) of top level posts about rationality and basketball (or sports in general). I’m partly holding off because I’m worried that the rationality aspects are too basic and obvious and no one else will care about the basketball parts.
But sports are great for talking about rationality because there is never an ambiguity about the results of our predictions and because there are just bucket-loads of data to work with. On the other hand, a surprising about of irrationality can be still be found even in professional leagues where being wrong means losing money.
Anyway, to answer your question: You get two kinds of information from play at the beginning of the game: First, you get information about what the final score will be from the points that have been scored already. So if my team is up 10 points the other team needs to score 11 more points over the remainder of the game in order to win. The less time remaining in the game the more significant this gets. The other kind of information is information about how the teams are playing that day. But if a team is playing significantly better or worse than you would have predicted coming in, their performance is most likely just noise. Regression to the mean is what should be expected. So my prediction of a team’s performance for the remainder of some game is going to be dominated by my priors (which hopefully are pretty sophisticated and based on a lot of data, for college basketball I start here and then adjust for a couple things that can’t be taken into account by that model (the way individual players match up against each other, injuries, any information about the teams’ mental states, etc.)
If you have all this information you can actually give, at any point during a game, the odds for you winning (there are a couple other factors that need to be considered as well, in particular you need to estimate how many possessions there will be in the rest of the game because the information we have about team performance is per/possession not per minute). I’ve also ignored fan attendance in this comment but that is really important evidence as well. I ended up attending the game in person and when I arrived I realized the venue included at least as many fans of the other team as there were fans of my team—and right there the probability my team was going to win dropped by 10%.