VideoThe other exception was a topic unlikely to be familiar to 21st-century Americans — the length of the reign of an Egyptian Pharaoh in the fourth millennium B.C. People consistently overestimated this, but in an interesting way. The analysis showed that the prior they were applying was an Erlang distribution, which was the correct type. They just got the parameters wrong, presumably through ignorance of political and medical conditions in fourth-millennium B.C. Egypt. On congressmen's term-lengths, which also follow an Erlang distribution, they were spot on.
Indeed, one of the most impressive things Griffiths and Tenenbaum have shown is the range of distributions the mind can cope with. Besides Erlang, they tested people with examples of normal distributions, power-law distributions and, in the case of baking cakes, a complex and irregular distribution. They found that people could cope equally well with all of them, cakes included. Indeed, they are so confident of their method that they think it could be reversed in those cases where the shape of a distribution in the real world is still a matter of debate.
To prove the point, they actually did such a reversal in the case of telephone-queue waiting times. Traditionally, these have been assumed to follow a Poisson distribution, but some recent research suggests they actually follow a power law. Analyzing the participants' responses suggests that a power law, indeed, it is.
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 behavior, 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.
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