## Bayes Theorem: A Real World Application

We all have learned about Bayes Theorem and its applications in statistics, but it is surprising to see how useful this rule is in real world applications.  When an Air France flight disappeared in the Atlantic Ocean in 2009, many different government agencies created a search team to sweep though and find the airplane.  At first they did the obvious and searched along the flight pattern.  However, when they were not able to find the plane or any signs of the plane along the expected flight path and the surrounding area, they were dumbfounded.  They now had a seemingly impossible task – to find a plane or signs of a plane in the entire Atlantic Ocean, or at least in a sizable portion of it.

To combat this problem, scientists developed a Bayesian model to predict the location of the plane.  The model took in factors such as the expected flight plan, weather, ocean currents, and other external factors.  The model then mapped a probability to a 50 mile radius around the expected crash zone.  Each point within this 5o mile circle was assigned a probability based on the models deemed probability of the plane being located here.  Obviously it can be seen that such a model/program will be useful in aided a search team to look for the plane, but how did the model work?

The model took in past/historical data on airplane flight patterns and deviations and used them to determine the probability of the plane’s location.  The mathematical definition of Bayes Theorm is the probability of A given B = the probability of B given A multiplied by the probability of A, this number is then divided by the probability of B. However, the Encyclopedia Britannica defines Bayes Theorem as “a means for revising predictions in light of relevant evidence, also known as conditional probability or inverse probability. ”  This is exactly what the model did using a large data set of information that was updated continuously as the search team entered results everyday after search a specific location.  Within days of implementing this model, the plane was found.  This shows how statistical models and theory can help improve efficiency in solving real-world problems.

http://www.npr.org/sections/thetwo-way/2014/03/25/294390476/can-a-250-year-old-mathematical-theorem-find-a-missing-plane

http://rldinvestments.com/Articles/BayesTheorem.html