Explore alternatives to simple probability change threshold

[danwahl]

Intuitively, it seems like it should be "harder" for markets to move to the limits of (0 or 1 ) than the middle (0.5). It might be possible to formalize this.

• Something very simple, like "it's equally surprising for a market to move 50% towards the limit in either direction."
• If numForecast(er)s is known for a given market, it could be modeled like a beta distribution, and some sort of hypothesis testing could be used to figure out how (un)likely an observed change is
  • However, many platforms don't provide numForecast(er)s, so at best this would have to be approximate
• There might be a way to Bayesian inference and conjugate priors to accomplish something similar?
• Maybe what we actually care about is information gain, e.g. Kullback–Leibler divergence or the Kolmogorov–Smirnov test?
• Something else entirely?

The above intuition may be wrong too, depending on something like what distribution new forecasts are sampled from.