Wednesday, September 28, 2016

First ClintonTrump Debate 092616 - Betting Markets

The betting market PredictIt on Tuesday morning showed virtually all shares predicting a Clinton victory trending upwards -- meaning that bettors thought the chances of her winning the White House had improved. Shares predicting a Trump victory, by comparison, lost value overnight.  Similarly, the betting site Hypermind showed Clinton’s likelihood of victory rising and Trump’s falling.

The well-regarded Predictwise site, which synthesizes data from multiple betting markets and more, registered one of the more dramatic shifts. Before the debate last night, it had Clinton with a 69 percent to 31 percent advantage is the race to win the White House. (That is measuring probability of an Electoral College victory, not the popular vote.) By Tuesday morning the divide had widened to 74-26 in Clinton’s favor.


That's a major pop aka "statistically significant"


Sunday, September 25, 2016

Logistic Function

A logistic function or logistic curve is a common "S" shape (sigmoid curve), with equation:

f(x)={\frac  {L}{1+{\mathrm  e}^{{-k(x-x_{0})}}}}
where
  • e = the natural logarithm base (also known as Euler's number),
  • x0 = the x-value of the sigmoid's midpoint,
  • L = the curve's maximum value, and
  • k = the steepness of the curve.[1]
For values of x in the range of real numbers from −∞ to +∞, the S-curve shown on the right is obtained (with the graph of f approaching L as x approaches +∞ and approaching zero as x approaches −∞).
The function was named in 1844–1845 by Pierre François Verhulst, who studied it in relation to population growth.[2] The initial stage of growth is approximately exponential; then, as saturation begins, the growth slows, and at maturity, growth stops.
The logistic function finds applications in a range of fields, including artificial neural networks, biology (especially ecology), biomathematics, chemistry, demography, economics, geoscience, mathematical psychology, probability, sociology, political science, linguistics, and statistics.

https://en.wikipedia.org/wiki/Logistic_function#Applications