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The Human Mind is a Bayes Logic Machine
lexxyz writes "Apparently the human mind can predict the distribution type for a given sample of results.
A study found in The Economist has shown that a group of minds working on single pieces of data, can together generate the statistical model used to represent a given sample. Note that it takes a group of people to be able to accurately predict the behaviour of something, not a single individual"
From the fine article:
Phew! Once I read that, I realized I didn't have to read the rest of the article having now taken a large enough "sparse" sample.An added benefit, I already know what all of the posts are going to say, including this one!
A study found in The Economist has shown that a group of minds working on single pieces of data, can together generate the statistical model used to represent a given sample. Note that it takes a group of people to be able to accurately predict the behaviour of something, not a single individual.
Well, that's a somehwat misleading summary. These people were not knowingly collaborating. Each person would have had to answer the questions independently (not knowing what the other respondants' answers were) in order for Bayes to be applicable. Each person's response counts as a piece of evidence or clue in inferring the underlying probability distribution. Their answers are combined using Bayes's rule by an external third party (the researchers). So, yes, this technically counts as a group of minds working together, but I think the way it this summary was worded might give people the wrong impression.
Think about it this way: if you lock a bunch of people in a room toegther and have them come up with an answer, the "strong" personalities in the room are likely to have a heavy influence on the "weaker" ones. People who aren't really firm in their opinions are going to influenced -- whether they realize it or not -- by people who sound confident. The article makes a big to-do about the fact that Bayesian techniques allow you to get good answers with a small number of people working on the problem. But the key is that those people have to be working independently because it's going to be damn difficult to identify and subtract out the cross-correlation of members influencing each other.
I'm making (what I hope to be) an important point. I think business people who read this article or even slashdotters who read the above summary may get the impression that small meetings are a great way to arrive at strikingly effective solutions. That's not what Bayes techinques are about. If you want to put a small group of people to work on a problem, you'd better separate them , otherwise Bayes's rule is not strictly applicable.
GMD
watch this
WOW!!
Imagine a beowulf cluster of these!!!
I call prior art on psychohistory
Furthermore, there is actually no solid evidence that the future exists
There is now.
It's not all about data and results. It's also about pre-formed boundaries, or domains within which answers usually (and some might say 'logically') fall.
This is one of those elementary, goosey sorts of tomes (if you RTFA) where a bunch of nerds go around with a bad hypthosis and come to an 'enlightened' conclusion.
Consider the techniques that surround Wolfram's expostuations-- that the world is algorhmic, and language ill-describes these algorithms, loosely defining them as processes. These setup boundaries within which we derive domains where answers must lay.
Proving that with just a few data points within a tight algorithm that you'll get the right answer is just hilarious-- of course you will. The domain fits, and so the answer must. The domain gets defined by a number of experience points as hidden references that allow the frequentists to get magic (e.g. hidden and historical) inferences to the answer. This is where the phenomenon of the trick question makes us all so frustrated.
My point? Inference has predefined boundaries, and so of course Bayesian logic doesn't require a bunch of data to lead to a correct conclusion because the boundaries are already so tightened that only those that randomly guess, and don't use historical data points (e.g. their freaking memories) are going to blow the answers.
Sigh.
---- Teach Peace. It's Cheaper Than War.
It wasn't stolen. He put it under his pillow and the sense of humor fairy left him a quarter.
It's not offtopic, dumbass. It's orthogonal.
Back in 1995, when I was at Carnegie Mellon, a researcher did a project in the planetarium at the Carnegie science museum. He had programmed a "joystick" to receive reflections from a set of reflective paddles held by the people in the audience. Each paddle had two different sides (red and green); depending on which side you held up, a different signal got sent back to the main processor (positive or negative, respectively). The overall "direction" taken by the game was determined by the sum of the responses - so if everyone held up "red", it as a 100% positive; but if everyone held up "green", it was 100% negative; and so on, with straight linear interpretation.
The first game was Pong. Up and down were controlled directly, if cumulatively, by the audience. You would think that control would be spotty, and that controls would overshoot. Instead, the audience was INCREDIBLY accurate in its overall response; even when the game got very fast, the audience played very, very well against the computer.
There were several games presented, but the last was a flight simulator, flying a plane through a set of rings. The left half of the audience controlled up and down; the right half controlled left and right. Again, you would think this would be nearly impossible to control - but the audience never missed a single ring, even when the game got fast.
Individually, it's doubtful that many members of the audience could have played any of the games as well as we saw the group play cumulatively. It was a clear and very effective demonstration that there was some sort of statistical model at play in the interplay of all those minds.
http://web.mit.edu/cocosci/Papers/prediction10.pd
It begins:
These questions have specific "right" answers, which can be achieved based on having the proper mental model for how lifespans and movie grosses are distributed. See how good a job you could do, without peeking, just based on your prior knowledge about the world.
Of course the future does not exist. It will exist though, just like the past existed.
"Wise men talk because they have something to say; fools, because they have to say something" - Plato
The "Scientific Method" is a myth perpetrated by elementary school science textbooks. Actual, practicing scientists (of which I am one) do not adhere to any cookbook "method", and in particular hypotheses (let alone their predictions) do not always precede data. In fact, it is quite common for it to be the other way around, especially when you don't know much about the system being studied (exploratory data analysis) or when new statistical methodologies allow you to reanalyze data in a better way.
Now, it is important to make new predictions about data that the hypothesis wasn't fit to, but a completely different issue is being discussed here. In fact, in this case the analysis method was decided upon before the data (not that it has to be); it's just that the data collection method was screwed: it allowed respondents to give non-numerical answers ("infinity") when the analysis method required finite positive values.
That's not because the statistical analysis method was made after the data was collected, it's because the statistical analysis method (p-values) are bogus; the inference method they're based on is not logically coherent. You can mathematically prove that the Bayesian method is coherent, and that p-values can grossly overestimate "significance".
Now, there are cases where the choice of statistical method has to be made before the data is taken (such as stopping rules in frequentist sampling theory), but those also arise because of incoherent methodology. Stopping rules, for instance, don't appear in any methodology that adheres to the likelihood principle (of which Bayesian methods are a subset).
One of the fundamental modern Bayesian papers is Jaynes' "How Does the Brain Do Plausible Reasoning?", which can be found on the web along with lots of other interesting things. Jaynes' conclusion is that we must be Bayesians under the skull. It's a compelling paper, even now.
These experimental results are exactly what Jaynes theory predicts, which is a very nice confirmation of his work. But they are not the "discovery" of anything--they are empirical confirmation of something we already knew. When light-bending by gravity was measured it was not a discovery, it was the confirmation of a theoretical prediction. This is the same.
Blasphemy is a human right. Blasphemophobia kills.
Ugh! There I go again.
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