Here is a quick look at how Bayesian statistics helped find Air France 447 in the Atlantic Ocean:
Stone and co are statisticians who were brought in to reëxamine the evidence after four intensive searches had failed to find the aircraft. What’s interesting about this story is that their analysis pointed to a location not far from the last known position, in an area that had almost certainly been searched soon after the disaster. The wreckage was found almost exactly where they predicted at a depth of 14,000 feet after only one week’s additional search…
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…
That’s an important point. A different analysis might have excluded this location on the basis that it had already been covered. But Stone and co chose to include the possibility that the acoustic beacons may have failed, a crucial decision that led directly to the discovery of the wreckage. Indeed, it seems likely that the beacons did fail and that this was the main reason why the search took so long.
The key point, of course, is that Bayesian inference by itself can’t solve these problems. Instead, statisticians themselves play a crucial role in evaluating the evidence, deciding what it means and then incorporating it in an appropriate way into the Bayesian model.
It is not just about knowing where to look – it is also about knowing how to look. Finding a needle in a haystack is a difficult business whether it is looking for small social trends in mounds of big data or finding a crashed plane in the middle of the ocean.
This could also be a good reminder that only having one search in such circumstances may not be enough. When working with data, failures are not necessarily bad as long as they can help move to a solution.