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January 8, 2006
A Bayesian Mind?
I've goofed around with Bayesian analysis at the intersection of archaeological and biblical studies. The Economist has an interesting article on the question of the extent to which our mind is a Bayesian reasoning machine. Here are a few snippets from the article.
The key to successful Bayesian reasoning is not in having an extensive, unbiased sample, which is the eternal worry of frequentists, but rather in having an appropriate “prior”, as it is known to the cognoscenti. This prior is an assumption about the way the world works—in essence, a hypothesis about reality—that can be expressed as a mathematical probability distribution of the frequency with which events of a particular magnitude happen.
With the correct prior, even a single piece of data can be used to make meaningful Bayesian predictions. By contrast frequentists, though they deal with the same probability distributions as Bayesians, make fewer prior assumptions about the distribution that applies in any particular situation. Frequentism is thus a more robust approach, but one that is not well suited to making decisions on the basis of limited information—which is something that people have to do all the time.
Thomas Griffiths of Brown University in Rhode Island and Joshua Tenenbaum of the Massachusetts Institute of Technology have been conducting a series of tests to determine if our normal reasoning works like a Bayesian machine. They think it does.
A key to a Bayesian analysis is what is known as the prior. The better the "prior" the better the judgment based on new data. I call the prior the "initial Bayesian probability" in my post on applying Bayesian analysis to the history of ancient Israel. One of the several things that interested me in the article was this,
How the priors are themselves constructed in the mind has yet to be investigated in detail. Obviously they are learned by experience, but the exact process is not properly understood. Indeed, some people suspect that the parsimony of Bayesian reasoning leads occasionally to it going spectacularly awry, with whatever process it is that forms the priors getting further and further off-track rather than converging on the correct distribution.That might explain the emergence of superstitious behaviour, with an accidental correlation or two being misinterpreted by the brain as causal. A frequentist way of doing things would reduce the risk of that happening. But by the time the frequentist had enough data to draw a conclusion, he might already be dead.
If this is correct, good non-reinforcing education may correct for a faulty "prior." In part because the full range of experience and knowledge builds on each previous "prior" to establish the "prior" for the next experience.
I'm not sure how all this will be accepted by the cognitive science community but I find the idea very attractive.
Via 3 Quarks Daily
Posted by Duane Smith at January 8, 2006 2:45 PM | Read more on Science - General |
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