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Does The NSA Think You Are A Terrorist?

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Does the NSA think you are a terrorist?

When the NSA sorts through American communications to find terrorists, what is their accuracy in identifying one?

One thing's for certain, No Test on earth is 100% accurate.

False Positive: an erroneous 'positive' diagnosis resulting from testing inaccuracies.

Let's assume the NSA's Terrorist test is 99% accurate (a very generous accuracy assumption).

False positive: 1 out of 100 'positive results' will actually be negative [misidentified].

If you receive a 'positive' then you are 99% likely to be a terrorist... right? <--WRONG.

The test will accurately measure 99% of terrorists who take it, NOT 99% of 'positive results' are terrorists.

This is a big difference and a common mistake.

True vs False positives - mathematicians use Bayes Theorem

1. Conditional Probability of an event A given an event B

Event A: Probability one is a Terrorist

Event B: Tested Positive by an accurate NSA test

2. Marginal probability of occurrence of each event (How rare are terrorists in America?)

Between 2001 and 2011 207 terrorist attacks were attempted within the United States - Average of 20.7 per year.

414 terrorists within America per year- (cautious assumption of 20 terrorists involved per attack.)

US population age 13+ is 258,458,870 people.

Marginal probability % American population that is a terrorist: 0.0001601802252% (1 in 624,297 americans are a terrorist).

Bayes Theorem

  • A = Probability of being a terrorist (low marginal probability)
  • ~A = Probability of not being a terrorist (high marginal probability)
  • X = 'Positive' Test Result
  • X|A = Probability 'Positive' Test Result given being a terrorist (Accurate test)
  • X|~A = Probability 'Positive' Test Result given not being a terrorist (Inaccurate Test)
  • Pr(A|X) = Probability of being a terrorist (A) given a positive test (X).

This is what we want to know: likelihood of having found a terrorist with a positive test result [plug in numbers]

.99 x 0.0000016 / (.99 x 0.0000016) + (.01 x 0.9999984) = 0.0001584 or 0.01584% Accurate (probability of being a terrorist given a 'positive' test result)

99.98416% false positive (probability of not being a terrorist given a 'positive' test result)

Surprised?

Higher the rarity, the more false results, despite an accurate test.

1 in 100 Marginal probability (rarity) - 50% accurate | 50% false positive

1 in 1,000 Marginal probability (rarity) - 9.0164% accurate |90.9836% false positive

1 in 100,000 - 0.0989% accurate | 99.9011% false positive

1 in 1,000,000 - 0.0098% accurate | 99.9902% false positive

In order for the NSA have a 94% probability of actually finding a terrorist with a 'positive' result the NSA testing methods would have to reach 99.9999% accuracy (equivalent to the accuracy of a DNA test).

How many False Positives have the NSA found?

We know that in just part of 2013, the government requested access to over 30,000 accounts of Americans from just 3 companies, which means that if each of these accounts represented a terrorist 98.62% would be false positives (remember 414 estimated terrorists on average in the last ten years).

Apple: December 1, 2012 to May 31, 2013 Apple received from U.S. between 4,000 and 5,000 info requests for Apple customer data.

Facebook: Of the 38,000 Facebook accounts targeted worldwide in the first half of this year, between 20,000-21,000 came from the US.

Google: At 8,438, the overwhelming majority of government requests originated in the US.

When it comes to living online... Never. Say. Anything.

SOURCES:
  1. http://www.start.umd.edu/start/publications/START_IUSSDDataTerroristAttacksUS_1970-2011.pdf
  2. http://www.census.gov/popclock/
  3. http://yudkowsky.net/rational/bayes/
  4. http://betterexplained.com/articles/an-intuitive-and-short-explanation-of-bayes-theorem/
  5. https://kiwi.ecn.purdue.edu/rhea/index.php/Bayes_theorem_eg2_S13
  6. http://www.cchem.berkeley.edu/molsim/personal_pages/berend/news/sim131.pdf
  7. https://www.apple.com/apples-commitment-to-customer-privacy/
  8. https://www.facebook.com/about/government_requests
  9. http://www.google.com/transparencyreport/userdatarequests/countries/?t=table


Does The NSA Think You Are A Terrorist?