How Bayes Rule Can Locate Missing Plane
Most people are familiar with the Malaysian plane carrying 239 that went missing on March 8th, 2014. It has been a hot news topic since, because no one has been able to locate the plane. Disasters like this are rare, yet have happened on occasion in the past. Several methods have been used to calculate the possible locations of these lost flights, including methods that use given information and past experiences. It makes sense that these methods have the best results because the more information one has about an event the easier it is to predict something about it. This ties directly to Bayes Theorem because it is a method for calculating conditional probability, using the reversed conditional probability and the probability of each event. For disasters such as this, each of these probabilities can be found by looking at past events. So if there is past information on events that occurred in this disaster, and there is given information from the plane before it was lost, Bayes Theorem can be used to calculate the probability of what happened to the plane.
Examples of past disasters include Air France Flight 447 which was lost for 2 years. This plane was found shortly after Bayes Theorem was applied to find the highest probabilistic location. Scientists gathered information about the flight at the time it was lost, such as the wind and water currents and used them as given information. The scientists were able to use past events and information to obtain the necessary probabilities for Bayes, and hence calculate the location of the plane. In the case of the Malaysian plane, similar calculations could result in finding the plane. Even if Bayes is not used for calculating the location, it can be used for calculating events that may have occurred which would influence the location. For example given the measured wind velocity and direction, they could calculate the probability that the plane crashed when it was lost. This would be: P(crash | wind velocity) = P(wind velocity | crash) P(crash)/ P(wind velocity). All of the components in the equation can easily be found by looking at past plane crashes and the wind velocity involved. A high probability would indicate it did crash immediately after it was lost, and physics calculations could find where the plane would have landed. Even with information lacking, the scientist’s “constant modification to a hypothesis” (Zahriyeh) is constantly updating Bayes, as they gain more information about past events to make the predictions more accurate. By taking and hypothesizing given information and probabilities, scientists can use Bayes Theorem to locate the missing plane.