Of Black Swans…
In 2001, Nassim Nicholas Taleb, quantitative trader and academician, published a book Fooled by Randomness where he outlined the theory of Black Swans. Taleb described black swans as events whose probability of occurrence was mathematically very low (like finding a black swan in a bevy of white swans). Taleb explained that these events occur with higher frequency than theory predicted, were hard to predict if not impossible to predict, and caused events of significant consequence and magnitude.
… and Dragon Kings
Sornette, on the other hand, makes an entirely contrary claim. Not only can he predict the probability of a bubble bursting, he can do it with remarkable accuracy and, of course, before the event! He calls these outlier events as Dragon Kings. He has graphs that show the predictions of the S&P 500 US Index, and oil prices made before the crash in 2007-08. These and others can be found on the website of his Financial Crisis Observatory.