The AstroStat Slog

I don’t know why astro-ph thought this article on the statistics of football dynamics (Mendes, Malacarne, Anteneodo 2007; physics/0706.1758) was relevant to me and emailed the abstract, but I’m glad they did, because they deal with a question I have wrestled with for a long time: how to figure out the underlying distribution that controls a stochastic process. In 2002ApJ…580.1118K, we dealt with modeling the photon arrival time differences as due to flares occuring at random times but with a power-law intensity distribution with index alpha. physics/0706.1758 deals with time-between-touches and tries to characterize that distribution itself in terms of a number of “phases” beta. From a quick reading, it appears that their beta are our flares, and they restrict all flares to have the same intensity. Despite the restriction, this is interesting because it is an analytical estimation that points a way towards speeding up our flare distribution fitting process, which currently is based on a Monte-Carlo grid search method, not the fastest way to do things.

Clauset, Shalizi, & Newman (2007, arXiv/0706.1062) have a very detailed description of what power-law distributions are, how to recognize them, how to fit them, etc. They are also making available their matlab and R codes that they use to do the fitting and such.

Looks like a very handy reference text, though I am a bit uncertain about their use of the K-S test to check whether a dataset can be described with a power-law or not. It is probably fine; perhaps some statisticians would care to comment?