People have proposed using price signals from prediction markets to estimate the odds of certain events. On Intrade right now, you can buy contracts for the two outcomes of the 2012 US Presidential Election. Each contract expires at $10 if the event occurs or $0 if it doesn’t. For example, “Barack Obama wins” contracts are $6.33 a pop right now, while “Mitt Romney wins” contracts go for $3.65. On the page, these are taken directly as probabilities, because it is assumed that the gamble is zero-sum.

Specifically, if \(p\) and \(\bar{p}=1-p\) are respectively the probabilities of two complementary events, and \(a\) and \(b\) are respectively the prices of contracts on them, which can be bought and sold freely, then no-arbitrage imposes that \(-a-b+10 = 0\) and statistical no-arbitrage imposes \(-\bar{p}a +p(10-a) = 0\) and \(-pb +\bar{p}(10-b) = 0\). Solving indeed gives the prices \(a=10p\) and \(b=10\bar{p}\).

However, this isn’t the end of the story.
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“The physicist-run Prediction Company is an example of a company that has apparently extracted unusual profits from the market for over a decade. In contrast, economist-run companies like LTCM and Enron have gone belly-up. Being a physicist certainly doesn’t guarantee success … but if you are going to look for correlations in (market or any other) data then being a physicist might help.”

Joseph L. McCauley, writing in
Dynamics of markets: econophysics and finance

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Nowadays there is a large amount of geological and seismic data collected. When earthquakes occur people try to do data analysis on this data to see if there are predictors. For example, there are people who look for foreshocks or changes in wave propagation, and so on. It seems to me that the next step beyond passive data collection would be to send active probe impulses to find the current condition of faults and whether they would fail soon. Is this done or not?

In any case, earthquake prediction may be a misnomer. One can never predict the precise time of an earthquake. But with more data and detection of ever smaller features, one can give more granular probabilistic predictions. So instead of saying there is a probability \(p\) of earthquake in the next 30 years, we may be able to either say (at any given moment) there is a probability \(p_1 \ll p\), or probability \(p_2 \gg p\) of one within the next year.

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