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The great physicist Enrico Fermi was known for his ability to make good guesses with little or bad data by multiplying series of estimates. 1

I've seen this described as corresponding to a stochastic process analogous to random diffusion of the square root of the step count on the logarithmic scale.

Do you agree, and if so how would you explain this to a layman?

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    I'm afraid that was the totality of detail given. It was noted in passing in an essay on another subject.2012-06-02

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Good description here: Wikipedia link

If estimate $F$ is a product of $n$ estimates (e.g. the Drake equation for number of possible intelligent civilizations in the universe)

$F=\prod_{i=1}^{n}f_{i}$

then

$\log F = \sum_{i=1}^{n}\log f_{i}$

if each estimate of $\log f$ is approximated as a normal distribution $N(\mu_i,\sigma_i)$ then we have a random-walk stochastic Weiner type process.

The layman can relate to a drunkard's walk ...