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Bayes' Theorem

Chapter 9: Bayes’ Theorem in Real Life: Search and Rescue

What if you were lost at sea? How could search and rescue find you?

In 2014 a missing fisherman was discovered using Bayes’ Theorem. It is a fascinating story that The New York Times reported on here and here, but we’ll sum it up for you below. Plus, we’ll also include an idea of how the theorem could have been used to find the missing individual.

Here’s the story:

John Aldridge is a fisherman who has fished for almost two decades. In 2006 Aldridge and his business partner Anthony Sosinski purchased their own boat and by 2014 had a successful crab and lobster operation. On July 24th of 2014 the partners were 40 miles off the coast of Long Island catching lobster. During the night while Sosinksi was sleeping, Aldridge was working and fell into the Atlantic. Using his rubber boots as pontoons, we managed to stay afloat in the 72-degree water until he was found almost 12 hours later by the Coast Guard.

To find Aldridge the Coast Guard used a piece of software called SAROPS (Search and Rescue Optimal Planning System). SAROPS creates a probability map that displays potential areas where survivors could be located based on input information. This map is then continually updated to reflect changes, additional clues, and areas where no survivors have been found. In Aldridge’s case, the Coast Guard only had two pieces of initial information to work with: a rough location and timeframe (he fell off his boat sometime during the evening of July 24th). Once this data had been uploaded into SAROPS, it was continually updated with ocean currents, new data from Sosinksi, clues and additional wind patterns.

A very simple form of how Bayes’ Theorem could be used in this situation is as follows. Please note that this is greatly simplified to demonstrate the possibility of using the theorem. In this example we have abbreviated the text:

  • P. Found = Person Found
  • Un. Search = Unsuccessful Search.

Again, the above is only a guess of how Bayesian Inference could be used in the search and rescue process. For more information, you can read more on SAROPS here. Wikipedia’s article on Bayesian Search Theory and this blog post are also helpful.

Bayes’ Theorem has been used in many search and rescue operations, including finding the USS Scorpion in 1968 and Air France Flight 447 in 2009.

Continue on to Chapter 10: Bayes’ Theorem in Real Life Uses: Spam Filtering.