Power laws and log-log plots II.

Back again to power laws. After some more googling, I found an even more important piece of blogging by Cosma Shalizi: Speaking Truth to Power About Weblogs, or, How Not to Draw a Straight Line. The title says it all: just don't play with power law distributions by fitting straight lines to log-log plots, because chances are that you will get a reasonably looking line and R squared will be relatively large, but that still does not mean that there is a power law distribution. Shalizi is complaining about papers in statistical physics and complexity theory that do such things -- well, he should see what is going on in sedimentary geology, where somebody invented the 'segmented power-law distributions' and now everybody who is measuring bed thicknesses is fitting not one, but two or even more straight lines to log-log plots of cumulative distributions. It's utter nonsense, even more so than with a single straight line, but it looks very sophisticated and regular, and people keep doing these plots and all kinds of fancy interpretations based on them (earthquakes, self-organizing criticality, confinement, erosion, etc.). If it plots as a straight line - fine, it's a power law, we explained everything. If it does not plot as a straight line -- well, just fit two straight lines and talk about two populations, and how the original power-law distribution has been modified by erosion, confinement, etc. - and we explained everything again. I know I am also guilty of some of this in my thesis, but at least I have never done the segmented power law plots.

Just for the records: here is a link to my paper in Sedimentology. Overall I am fairly happy with it, I haven't changed my mind about most of the things I have written about in this paper, unlike with many other subjects I have done some work on.

Power laws and log-log plots I.

Did a bit of reading today on power law distributions, just to refresh my memories from three years ago when I was writing my thesis. And found some interesting papers and notes on the web, e.g., this one. I think we are still far from being able to use bed thickness distributions in a useful, predictive way, even though this has become a popular subject among turbidite experts. One of the problems is that it is easy to play with the distributions (e.g., take an initial power-law distribution and modify it by amalgamation), but things are probably a lot more complicated and cannot be explained just with amlagamation and basin topography. The other problem is that power-law distributions and their exponents cannot be assessed by fitting a straight line to an exceedence probability plot, as it is explained here. This method is bound to give erroneous estimates when dealing with a single distribution, but it is close to meaningless when people want to break out two different populations by fitting not one, but two lines to the exceedence probability plot.

Well, I guess that is enough about power laws for today.