## Terrorists, Data Mining, and the Base Rate Fallacy

I have already explained why NSA-style wholesale surveillance data-mining systems are useless for finding terrorists. Here's a more formal explanation:

Floyd Rudmin, a professor at a Norwegian university, applies the mathematics of conditional probability, known as Bayes' Theorem, to demonstrate that the NSA's surveillance cannot successfully detect terrorists unless both the percentage of terrorists in the population and the accuracy rate of their identification are far higher than they are. He correctly concludes that "NSA's surveillance system is useless for finding terrorists."The surveillance is, however, useful for monitoring political opposition and stymieing the activities of those who do not believe the government's propaganda.

What is the probability that people are terrorists given that NSA's mass surveillance identifies them as terrorists? If the probability is zero (p=0.00), then they certainly are not terrorists, and NSA was wasting resources and damaging the lives of innocent citizens. If the probability is one (p=1.00), then they definitely are terrorists, and NSA has saved the day. If the probability is fifty-fifty (p=0.50), that is the same as guessing the flip of a coin. The conditional probability that people are terrorists given that the NSA surveillance system says they are, that had better be very near to one (p=1.00) and very far from zero (p=0.00).The mathematics of conditional probability were figured out by the Scottish logician Thomas Bayes. If you Google "Bayes' Theorem", you will get more than a million hits. Bayes' Theorem is taught in all elementary statistics classes. Everyone at NSA certainly knows Bayes' Theorem.

To know if mass surveillance will work, Bayes' theorem requires three estimations:

- The base-rate for terrorists, i.e. what proportion of the population are terrorists;

- The accuracy rate, i.e., the probability that real terrorists will be identified by NSA;

- The misidentification rate, i.e., the probability that innocent citizens will be misidentified by NSA as terrorists.
No matter how sophisticated and super-duper are NSA's methods for identifying terrorists, no matter how big and fast are NSA's computers, NSA's accuracy rate will never be 100% and their misidentification rate will never be 0%. That fact, plus the extremely low base-rate for terrorists, means it is logically impossible for mass surveillance to be an effective way to find terrorists.

I will not put Bayes' computational formula here. It is available in all elementary statistics books and is on the web should any readers be interested. But I will compute some conditional probabilities that people are terrorists given that NSA's system of mass surveillance identifies them to be terrorists.

The US Census shows that there are about 300 million people living in the USA.

Suppose that there are 1,000 terrorists there as well, which is probably a high estimate. The base-rate would be 1 terrorist per 300,000 people. In percentages, that is .00033%, which is way less than 1%. Suppose that NSA surveillance has an accuracy rate of .40, which means that 40% of real terrorists in the USA will be identified by NSA's monitoring of everyone's email and phone calls. This is probably a high estimate, considering that terrorists are doing their best to avoid detection. There is no evidence thus far that NSA has been so successful at finding terrorists. And suppose NSA's misidentification rate is .0001, which means that .01% of innocent people will be misidentified as terrorists, at least until they are investigated, detained and interrogated. Note that .01% of the US population is 30,000 people. With these suppositions, then the probability that people are terrorists given that NSA's system of surveillance identifies them as terrorists is only p=0.0132, which is near zero, very far from one. Ergo, NSA's surveillance system is useless for finding terrorists.

Suppose that NSA's system is more accurate than .40, let's say, .70, which means that 70% of terrorists in the USA will be found by mass monitoring of phone calls and email messages. Then, by Bayes' Theorem, the probability that a person is a terrorist if targeted by NSA is still only p=0.0228, which is near zero, far from one, and useless.

Suppose that NSA's system is really, really, really good, really, really good, with an accuracy rate of .90, and a misidentification rate of .00001, which means that only 3,000 innocent people are misidentified as terrorists. With these suppositions, then the probability that people are terrorists given that NSA's system of surveillance identifies them as terrorists is only p=0.2308, which is far from one and well below flipping a coin. NSA's domestic monitoring of everyone's email and phone calls is useless for finding terrorists.

As an exercise to the reader, you can use the same analysis to show that data mining is an excellent tool for finding stolen credit cards, or stolen cell phones. Data mining is by no means useless; it's just useless for this particular application.

Posted on July 10, 2006 at 7:15 AM • 143 Comments

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