In the case of Air France Flight 447, the underlying distribution was the probability of finding the wreckage at a given location. That depended on a number of factors such as the last GPS location transmitted by the plane, how far the aircraft might have traveled after that and also the location of dead bodies found on the surface once their rate of drift in the water had been taken into account.Way cool.
All of this is what statisticians call the “prior.” It gives a certain probability distribution for the location of the wreckage.
However, a number of searches that relied on this information had failed to find the wreckage. So the question that Stone and co had to answer was how this evidence should be used to modify the probability distribution.
This is what statisticians call the posterior distribution. To calculate it, Stone and co had to take into account the failure of four different searches after the plane went down. The first was the failure to find debris or bodies for six days after the plane went missing in June 2009; then there was the failure of acoustic searches in July 2009 to detect the pings from underwater locator beacons on the flight data recorder and cockpit voice recorder; next, another search in August 2009 failed to find anything using side-scanning sonar; and finally, there was another unsuccessful search using side-scanning sonar in April and May 2010.
Wednesday, May 28, 2014
Finding Air France--Call In The Statisticians
Having taken some recent courses in statistics I can better understand this article about finding the Air France airliner two years after it crashed into the Atlantic. Bayesian inference, prior distribution, posterior distribution--I get these! Yes, you can understand their meaning in context, but I understand the math behind them and it makes this article even more interesting: