Finding People Lost at Sea With Bayes Theorem
https://www.bayestheorem.net/real-life-uses-search-and-rescue/
In this article, we find a story of how a man was found lost at sea with the help of Bayesian principles. Essentially, on July 24th, 2014 a fisherman for almost two decades, John Aldridge, was working on his boat for his successful crab and lobster operation when he accidentally fell into the Atlantic oceans. For almost 12 hours, John kept himself afloat at sea using his rubber boots as pontoons to keep himself afloat. To find him, the Coast Guard used a program called the Search and Rescue Optimal Planning System or SAROPS for short. This program created probability maps that used inputted information to find areas where the survivors could probably be found and where there were probably no survivors. The information that they put into SAROPS were the rough location and time that he fell off the boat, ocean currents, and wind patterns, which SAROPS then used to process its Bayesian probabilities and to find the probability of the person actually being in an area that was actually previously unsuccessfully searched. In a simplified version, two probabilities were essentially formed, P(A) and P(X), the probability of the person being in a certain area and the probability of an unsuccessful search in that area, where that area was searched but rescuers did not find anything. So, the Bayes theorem in this scenario turned out to be P(A | X) = (P(X | A) x P(A)) / P(X). In this case, the probability of a failed search given that the person was actually there and the probability that the person was there was calculated by SAROPS, so the coast guard had found P (X | A) and P (A). However, figuring out the probability of an unsuccessful search was a little more tricky and to find this number, they had to use Bayes theorem to expand the denominator P (X). So, they realized that the probability of an unsuccessful search equaled the probability of an unsuccessful search given the person was there multiplied by the probability the person was there added by the probability of an unsuccessful search given the person was not there (which is actually 1) multiplied by the probability that the person was not there. So, now SAROPS had all the data it needed to find a complete Bayes Theorem prediction of where John would most likely be, and this use of Bayes Theorem aided the Coast Guard in their efforts to rescue John which they managed to do just 12 hours after his disappearance.