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<math>P \left({A_1 \cup A_2}\right) = P\left({A_1}\right) + P\left({A_2}\right) -P \left({A_1 \cap A_2}\right)</math>
<math>P \left({A_1 \cup A_2}\right) = P\left({A_1}\right) + P\left({A_2}\right) -P \left({A_1 \cap A_2}\right)</math>


==Derek Jeter==
==Ebola quanrantines==
[http://www.nytimes.com/2014/10/13/opinion/how-to-quarantine-against-ebola.html?action=click&contentCollection=Soccer&module=RelatedCoverage&region=Marginalia&pgtype=article How to quarantine against Ebola]<br>
[http://www.nytimes.com/2014/10/13/opinion/how-to-quarantine-against-ebola.html?action=click&contentCollection=Soccer&module=RelatedCoverage&region=Marginalia&pgtype=article How to quarantine against Ebola]<br>
by Siddartha Mukherjee, ''New York Times'',13 October 2014  
by Siddartha Mukherjee, ''New York Times'',13 October 2014  

Revision as of 13:12, 15 October 2014

Some math doodles

<math>P \left({A_1 \cup A_2}\right) = P\left({A_1}\right) + P\left({A_2}\right) -P \left({A_1 \cap A_2}\right)</math>

Ebola quanrantines

How to quarantine against Ebola
by Siddartha Mukherjee, New York Times,13 October 2014

This op-ed piece dismisses several strategies for containing entry and spread of Ebola in the U.S. in favor of blood-sample screening based on multiplying any genes of the virus present via PCR (polymerase chain reaction).

Author Mukherjee (a professor of medicine at Columbia University) cites a false-positive rate of 3 per thousand and a false-negative rate of 4 per thousand.

Discussion

1. If an average of one person per planeload of 200 people has contracted the Ebola virus, what is the ratio of false positives to true positives in screening such planeloads?

2. If one in 1,000 people screened has the Ebola virus, what is the ratio of false positives to true positives?

3. If one in 10,000 people screened has the Ebola virus, what is the ratio of false positives to true positives?

4. Dr. Mukherjee cites a 2000 study in The Lancet of 24 "asymptomatic" individuals who had been exposed to Ebola. They were tested for the Ebola virus using an earlier version of the proposed screening test. Of the 24: ---11 developed Ebola, 7 of whom had had positive tests; ---13 did not develop Ebola, and none of them had tested positive. From these data, how would you estimate the false-positive rate and false-negative s (with appropriate measures of uncertainty)? (The rates 3/1000 and 4/1000 cited above are for a later version of the method as refined in 2004.)

Submitted by Paul Campbell

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.

BrokenTile.jpg

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 % of 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%
Montante plot1.png

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” and “Chance favors only the prepared mind.”

Montante plot2.png

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. Shattered eggs reveal secrets of explosions. As described there, 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. Seems there is a science underpinning how things break and explode; potentially useful in Forensic reconstructions. Bill also provided a link to a vignette from CRAN describing a maximum likelihood procedure for fitting a Power Law relationship. I am now learning my way through that.

Submitted by William Montante