How an Eighteenth-Century Statistician Is Helping to Find MH370By
The 18th-century statistician behind the latest search for Malaysia Airlines Flight 370 is so influential in modern-day logic that his work has been used to show the existence of God.
After hunting in vain for almost two years, Australian authorities said Thursday they’ve narrowed down the missing jet’s most likely location to a new “hot spot” in the southern part of a 120,000 square kilometer zone. Bayesian analysis, based on the probability theory of Thomas Bayes, has proved central to mapping out the probable resting place of the aircraft.
The Australian Defence, Science and Technology Group used Bayes’ statistical approach to crunch data on satellite communications, aircraft dynamics and the environment to refine the search area.
So why has an idea developed by an English Presbyterian minister become so important centuries after his death in 1761?
Bayes’ law or rule, as it’s now known, describes the probability of an event taking place once other conditions are taken into account. Those conditions might include previous studies and experiments, or even human bias weighing on the data.
At the heart of the approach is the quantification of uncertainties -- calculations that are continually updated as new information arises.
“It’s a very natural learning cycle,” said Kerrie Mengersen, a professor at the Queensland University of Technology in Brisbane who has studied Bayesian statistics for more than 20 years. “It allows in a very repeatable way the inclusion of different sources of information.”
Modern computer-processing power now allows us to calculate the uncertainties that Bayes once theorized, making the approach helpful in a range of areas from medicine and genetics to defense and finance, said Mengersen.
Bayesian analysis has permeated financial markets. Former Federal Reserve Board Chairmen Alan Greenspan and Ben S. Bernanke and current Australian central bank Governor Glenn Stevens have all acknowledged the influence of Bayes on policy making.
In his 2003 book, The Probability of God, Stephen D. Unwin ran Bayes’ equation to argue that God exists. The technique helped find the lost nuclear submarine USS Scorpion in 1968 and was used in the successful search for Air France Flight 447, almost two years after it plunged into the Atlantic Ocean in 2009.
They estimated the distance the plane traveled from its last known position by looking at nine other accidents involving loss of control. Thirty-three recovered bodies were reverse-tracked to the moment of impact by assessing winds and currents. And unsuccessful underwater sonar searches also featured in the math, building in the chance that the plane’s locator beacons weren’t actually emitting a signal.
The wreckage was eventually discovered near the center of Metron’s highest-probability zone.
A counter-intuitive probability puzzle called the Monty Hall problem is still taught today to demonstrate Bayes’ rule in action. It’s named after the host of the 1960s U.S. television game show, "Let’s Make a Deal."
The contestant is given the choice of three doors. Behind one door is a car. Behind the other two, goats. The contestant chooses door No. 1. Then the host, who is aware of where the car is, opens No. 2 to reveal a goat. He offers the contestant the chance to switch from No. 1 to No. 3. Should he change his mind?
Door No. 1 always had a 1-in-3 chance of success. A Bayesian approach would conclude that by eliminating door No. 2 -- new information -- door No. 3 now carries a 2-in-3 chance of success. So the contestant should switch to door No. 3.
“The very first time I heard it, I said: ‘you’re joking,”’ said Mengersen at Queensland University of Technology. “But when you do the calculations, you change your mind.”
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