  The massive diffusion of online social media allows for the rapid and
uncontrolled spreading of conspiracy theories, hoaxes, unsubstantiated claims,
and false news. Such an impressive amount of misinformation can influence
policy preferences and encourage behaviors strongly divergent from recommended
practices. In this paper, we study the statistical properties of viral
misinformation in online social media. By means of methods belonging to Extreme
Value Theory, we show that the number of extremely viral posts over time
follows a homogeneous Poisson process, and that the interarrival times between
such posts are independent and identically distributed, following an
exponential distribution. Moreover, we characterize the uncertainty around the
rate parameter of the Poisson process through Bayesian methods. Finally, we are
able to derive the predictive posterior probability distribution of the number
of posts exceeding a certain threshold of shares over a finite interval of
time.
