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MH370: Could Maths Equation Used By Tech Companies Help?

Microsoft and Google have used an 18th century math theorem to drive their innovations. Could it be used to find the wreckage of the Malaysian plane MH370, now assumed to have crashed in the southern Indian Ocean?  Ayesha Salim investigates.

During the 18th century, a Presbyterian minister by the name of Thomas Bayes could not have imagined his math theorem would form the basis of much of the technology that we know today. In fact, after his breakthrough, Bayes lost faith in his theorem and abandoned it, and it took Pierre Simon Laplace, a major figure in the development of mathematics astronomy and statistics, to discover a version and advance it into its current form. Now the theorem has grown indispensable to tech companies and could be the key to finding the black box from flight MH370.

There are quite a few explanations of Bayes’ rule. But the general rule is this: By updating our initial belief about something with objective new information, we get a new and improved belief.

 

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 Above: Formula for Bayes' theorem

I got in touch with Sharon McGrayne, author of The Theory That Would Not Die, so she could explain it in more detail.

“Bayes' rule says we can start off thinking about a hypothesis (even if we don't know how realistic or probable it is) but it commits us to updating or modifying that hypothesis every single time a new piece of information arises. After a while, we will have a much more realistic and probable hypothesis. At that point, we may have to -- imagine this! -- change our minds!’

“With powerful computers to update and modify our hypothesis every time new knowledge arises, Bayes' rule can be very powerful.” McGrayne adds.

It turns out that Bayes’ rule has been used throughout history, and in recent times, to locate the Air France plane in 2011 which was missing for two years. As McGrayne tells me: 

“Once the Bayesians analyzed all the evidence compiled during two years of searching, they were able to identify the most probable location of AF447's wreckage -- where it was found after an undersea search of one week”.

Is the Bayesian theory being used now to locate the flight recorder of flight MH370?

McGrayne : “In the beginning it was not being used, I feel sure -- and Bayesian search experts told me that. However, three members of the French team that hired and worked with Metron's Bayesians went to Malaysia early this week. So I'm sure they will be trying to use Bayesian methods. The search will not be easy or quick, though.”

There have been sightings of floating objects in the southern Indian Ocean which could be linked to flight MH370. But investigators face the challenging task of figuring out how far and where a floating object traveled over two weeks in the Indian Ocean. Plus the tough search conditions will not help either. I wonder if this can complicate the Bayesian calculations and estimates.

McGrayne doesn’t seem to think so.

“Bayes' rule is meant to deal with uncertainties. That's its claim to fame. If we knew where the plane was, we wouldn't need Bayes.”

But according to Bradley Efron, Professor of Statistics at Stanford, the situation in comparison to the Air France flight is much trickier.

“Bayes’ theorem is often a good way to organize evidence that arrives in a sequential fashion. For flight 447, they may have started out with a prior distribution putting equal weight over a wide swath of the Atlantic, and then Bayesianly updated [the hypothesis] with each new piece of evidence. For instance, not seeing anything on a reconnaissance flight would down weight the probability on the part of the ocean covered. Spotting some possible wreckage would up weight probability in that vicinity. I don't know if that was what was done with 447.

“The situation is messier for MH370. Bayes theorem is less useful in situations where there are major paradigm changes as time goes on,” Efron says.

Bayes’ rule may have come into the limelight when it was used to find the flight 447 but it has been used throughout history.

McGrayne: “Bayes' rule has been developed over the past 70 years to find airplanes, mines, bombs, submarines, ships, etc.”

“It was first used for searching during World War II to locate German submarines sinking unarmed merchant marine ships in the North Atlantic Ocean. Most spectacularly it was used to hunt and find Soviet submarines cruising the Mediterranean and Atlantic,” McGrayne says.

Incredibly, Bayes’ rule has formed the basis for innovations driving tech today. Bill Gates claimed Microsoft’s competitive advantage lay in its expertise in ‘Bayesian networks’. Google has been known to use the Bayesian system in its ‘driverless cars’ and the Bayesian model has also been used by Autonomy and Netflix. It was even used to accurately predict the outcome of the presidential vote in all 50 states. The list is endless. Bayes could not have predicted how influential his theorem would become in modern technology but it has clearly cemented its position – and might just be the key to recovering the black box from flight MH370. 

 

Ayesha Salim is e-Content Writer at IDG Connect

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Ayesha Salim

Ayesha Salim is Staff Writer at IDG Connect

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