## Bayes Theorem and Finding Flight 370

http://fivethirtyeight.com/features/how-statisticians-could-help-find-flight-370/

The article describes how statisticians can apply Bayes Theorem to help locate the missing Malaysia Airlines Flight 370 plane. It starts with a basic description of Bayes Theorem, and how it can be applied to real world scenarios. This is relevant to our class as we also discussed Bayes Theorem and its applications. In our discussions it has been limited to simple situations, with only two events. The article describes how Bayes Theorem can be applied multiple times to find the probability of more complex situations. This is seen in the example of finding the probability of getting a good meal at a restaurant. They apply Bayes Theorem multiple times in succession as new pieces of information become available. The result is a more accurate prediction, that fully utilizes all of the available data.

After describing the basics of Bayes Theorem, the article continues to state how it can assist the search for the lost plane. In this case, the plane could be in many possible locations. We are more interested in the probability distribution of an area in the ocean. The article makes the reasonable assumption that the plane is equally likely to be at any point (that is close to the flight path). Data from beacons is then used in conjunction with Bayes Theorem to determine the likelihood that a beacon search would find the wreckage if it was within the beacon’s search area. The article then continues in describing objections to utilizing Bayes Theorem for this problem. One argument being that there is an intrinsic error in the calculated probability, due to an accumulation of error in estimations of the probability of individual events. Despite these objections, Bayes Theorem is a useful tool that helps to quantify the problem of finding a crashed plane.