Descriptive statistics vs. inferential probabilities

It seems that they are often misused in the literature of many fields, often with no distinction between them at all and treating them implicitly as the same thing. For example, the much exalted power law distributions are touted as awesome and a good way to explain phenomena, but their value seem to be pretty low and limited since they are only descriptive in nature - you are fitting historical data based on potentially very different conditions than what can occur in the future. There was even a TED talk on this about the power law between the frequency vs. severity of deaths in Iraq. Seems that once you write them down, power laws are essentially useless as a guide to choose the correct decision for the future, most relevantly for trading or investing. Also, seems that it would take some effort to show that something did “not” follow a power law distribution, especially since: - you are using log-log plots where the eye can easily be fooled - errors at one scale that may be huge are trivial at another scale at different orders of magnitude For those with more familiarity descriptive statistics, inferential probabilities, and power laws: - where am I wrong or limited in my thinking? - can you comment on specific cases in the literature? Thanks in advance.

I saw the TED talk that referenced the power law and deaths in Iraq. I thought it was one of the worst TED talks I’d ever seen. As a trained social scientist who has pretty good knowledge of the natural sciences, it seemed so ridiculous for this physicist to jump up and down saying, “look, I plotted it on a log-log chart, and it’s sorta linear!! Physics is awesome! We’re SO much better than other sciences. No one else could POSSIBLY have told us that we’ll have lots and lots of small incidents and a few large ones.” I’m pretty sure that any second year polisci undergrad worth his/her salt could probably have told you the qualitative outcome. Now, if he had a method to predict the slope of that graph, using things other than his intuition, now THAT would have been impressive. As it was, though, it was just handwaving and self congratulations. Quants in finance are better than this guy at getting perspective on things, although not all of them.

I totally agree with you bchadwick. That physicist was a Rhodes scholar too! Of course, that award, any number of Nobel prizes, or any other award does not prevents him from being incorrect or allows him to say things that are more truthful than anyone even if they might be smarter than me. I’m seeing these power law conclusions creep up everywhere and I totally don’t buy them, especially when there aren’t a lot of data points to fit and when fitting spans multiple orders of magnitude. Karl Popper and George Soros say that one important feature of science is that one can invalidate a theory. This is a powerful view of science and I do agree with that, but with the qualification that I am not a philosopher of science so I may be missing many things. It appears in these power laws that now we have moved to a “meta” level, to the “method” of going about science. There doesn’t seem to me at this moment a clear way to invalidate the “method” of bogus power law claims.

Do any power law models actually claim to be predictive of market direction in anyway or over any specified time frame? Earthquakes maybe, but markets? I haven’t seen a model that is useful for investing. Maybe somewhat for risk management, but even then: show me it is predictive/useful.

I agree with you eureka, power laws seem of very low value and full of tautologies. I also rewatched the video and am disgusted by how much this guy is so self-satisfied with being a physicist. Karl Popper and George Soros (paraphrased): “Not only can we be wrong, we are bound to be wrong.”

I like to do some descriptive statistics with subs mom

If something looks like it has a power law distribution, then I think that knowledge could be useful for risk management purposes. I wouldn’t think it’s terribly useful for predictive purposes, however.

Agreed with you on the Iraq death TED talk. One of my fellow students in my masters program sent it out to us and I tore into him about how dumb it was. He thought it was so cool that war could be modeled, showcasing hippie ignorance to the fact that it’s been modeled by highly paid and accredited intelligence analysts in war rooms since the 80’s. That aside, I also believe that while power laws are interesting, by their nature they offer very low predictive quality. It’s more of a rephrasing of EMH than anything (in terms of market unpredictability, not market correctness). Whereas statistics based upon historical analysis or normal / stationary assumptions offers some very precise predictions. I guess the middle ground that must be reached is that power law guys like me need to admit our science is essentially useless with the exception of testing the robustness of organizational risk structures, while quant traders and the like need to remain ever cognicent (and not be lulled into complacancy) to the fact that beneath their models lies a non-normal, non-stationary universe. While fractal geometry is what I would like to study, I’m concerned that when I complete graduate studies in the subject, I’ll have accrued yet another useless degree as it may have limited practical application within finance. In the end the only truly robust risk solution that would properly mitigate the threat of large shifts is to delever and/or simplify financial instruments and essentially become large commercial banks. We all know this will never happen as long as we remain a biological system of freely acting individuals with human behavioral traits and the desire to dream big.

Check this out! Aaron Clauset, Cosma Rohilla Shalizi, M. E. J. Newman Power-law distributions in empirical data

Their conclusion… The study of power laws spans many disciplines, including physics, biology, engineering, computer science, the earth sciences, economics, political science, sociology, and statistics. Unfortunately, well founded methods for analyzing power-law data have not yet taken root in all, or even most, of these areas and in many cases hypothesized distributions are not tested rigorously against the data. This naturally leaves open the possibility that apparent power-law behavior is, in some cases at least, the result of…WISHFUL THINKING.