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Accidental Insights
My collective understanding of Power Laws would fit beneath the shallow end of the long tail. Curiosity, however, easily fills the fat end.  I long have been intrigued by the concept and the surprisingly common appearance of power laws in varied natural, social and organizational dynamics.  But, am I just seeing a statistical novelty or is there meaning and utility in Power Law relationships? Here’s a case in point.
While carrying a pair of 10 lb. hand weights one, by chance, slipped from my grasp and fell  onto a piece of ceramic tile I had left on the carpeted floor. The fractured tile was inconsequential, meant for the trash. As I stared, slightly annoyed, at the mess, a favorite maxim of the Greek philosopher, Epictetus, came to mind: “On the occasion of every accident that befalls you, turn to yourself and ask what power you have to put it to use.”  Could this array of large and small polygons form a Power Law? With curiosity piqued, I collected all the fragments and measured the area of each piece.
Piece Sq. Inches % Total
1 43.25 31.9%
2 35.25 26.0%
3 23.25 17.2%
4 14.10 10.4%
5 7.10 5.2%
6 4.70 3.5%
7 3.60 2.7%
8 3.03 2.2%
9 0.66 0.5%
10 0.61 0.5%
The data and plot look like a Power Law distribution. The first plot is an exponential fit of percent total area. The second plot is same data on a log normal format. Clue: Ok, data fits a straight line.  I found myself again in the shallow end of the knowledge curve. Does the data reflect a Power Law or something else, and if it does what does it reflect?  What insights can I gain from this accident? Favorite maxims of Epictetus and Pasteur echoed in my head:
“On the occasion of every accident that befalls you, remember to turn to yourself and inquire what power you have to turn it to use.”
“Chance favors only the prepared mind.”
My “prepared” mind searched for answers, leading me down varied learning paths. Tapping the power of networks, I dropped a note to Chance News editor Bill Peterson. His quick web search surfaced a story from ''Nature News'' on research by Hans Herrmann, et. al. Seems there is a science underpinning how things break and explode; potentially useful in Forensic reconstructions. “”
[http://www.nature.com/news/2004/040227/full/news040223-11.html Researchers have found power-law relationships for the fragments produced by shattering a pane of glass or breaking a solid object, such as a stone].  Bill also provided a link to [http://cran.r-project.org/web/packages/poweRlaw/vignettes/poweRlaw.pdf a paper from CRAN] describing the preferred method for determining a Power Law relationship. I am now learning my way through that.
==Interpreting climate change probabilities==
==Interpreting climate change probabilities==
Bob Griffin sent a link to the following
Bob Griffin sent a link to the following

Revision as of 16:29, 18 July 2014

Accidental Insights

My collective understanding of Power Laws would fit beneath the shallow end of the long tail. Curiosity, however, easily fills the fat end. I long have been intrigued by the concept and the surprisingly common appearance of power laws in varied natural, social and organizational dynamics. But, am I just seeing a statistical novelty or is there meaning and utility in Power Law relationships? Here’s a case in point. While carrying a pair of 10 lb. hand weights one, by chance, slipped from my grasp and fell onto a piece of ceramic tile I had left on the carpeted floor. The fractured tile was inconsequential, meant for the trash. As I stared, slightly annoyed, at the mess, a favorite maxim of the Greek philosopher, Epictetus, came to mind: “On the occasion of every accident that befalls you, turn to yourself and ask what power you have to put it to use.” Could this array of large and small polygons form a Power Law? With curiosity piqued, I collected all the fragments and measured the area of each piece. Piece Sq. Inches % Total 1 43.25 31.9% 2 35.25 26.0% 3 23.25 17.2% 4 14.10 10.4% 5 7.10 5.2% 6 4.70 3.5% 7 3.60 2.7% 8 3.03 2.2% 9 0.66 0.5% 10 0.61 0.5%



The data and plot look like a Power Law distribution. The first plot is an exponential fit of percent total area. The second plot is same data on a log normal format. Clue: Ok, data fits a straight line. I found myself again in the shallow end of the knowledge curve. Does the data reflect a Power Law or something else, and if it does what does it reflect? What insights can I gain from this accident? Favorite maxims of Epictetus and Pasteur echoed in my head: “On the occasion of every accident that befalls you, remember to turn to yourself and inquire what power you have to turn it to use.” “Chance favors only the prepared mind.”


My “prepared” mind searched for answers, leading me down varied learning paths. Tapping the power of networks, I dropped a note to Chance News editor Bill Peterson. His quick web search surfaced a story from Nature News on research by Hans Herrmann, et. al. Seems there is a science underpinning how things break and explode; potentially useful in Forensic reconstructions. “” Researchers have found power-law relationships for the fragments produced by shattering a pane of glass or breaking a solid object, such as a stone. Bill also provided a link to a paper from CRAN describing the preferred method for determining a Power Law relationship. I am now learning my way through that.


Interpreting climate change probabilities

Bob Griffin sent a link to the following

The interpretation of IPCC probabilistic statements around the world
by David V. Budescu, et al, Nature Climate Change, 20 April 2014

which he describes as "an intriguing look at how folks in different cultures around the world interpret the verbal statements of uncertainty that the Intergovernmental Panel on Climate Change uses. They found that an alternative presentation format (verbal terms with numerical ranges) improves the correspondence between the IPCC guidelines and public interpretations. The alternative presentation format also produces more stable results across cultures."

On the Nature site, only the abstract is available to non subscribers, but you can read more about the study design in this Fordham University press release. As described there:

The study asked over 11,000 volunteers in 24 countries (and in 17 different languages) to provide their interpretations of a the intended meaning and possible range of 8 sentences form the IPCC report that included the various phrases. For example, one sentence read: “It is very likely that hot extremes, heat waves, and heavy precipitation events will continue to become more frequent.” Only a small minority of the participants interpreted the probability of that statement consistent with IPCC guidelines (over 90 percent), and the vast majority interpreted the term to convey a probability in around 70 percent.

Similar patterns were found with other phrases. When verbal descriptions were used without numerical ranges, readers tended to interpret the probabilities as being closer to 50 percent than intended by the guidelines.

Reproducibility

When studies are wrong: A coda
by George Johnson, New York Times, 7 March 2014


Submitted by Bill Peterson

Finding lost aircraft

Jeanne Albert sent a link to the following

How statisticians found Air France Flight 447 two years after it crashed into Atlantic
MIT Technology Review, 27 May 2014

How statisticians could help find that missing plane, by Carl Bialik, FiveThirtyEight, 17 March 2014