Note: this post was revised and expanded during the morning of 20 March 2014.
What happened to Malaysia Airlines Flight 370? Specifically, do you have any “priors” about what may have happened, e.g. sabotage, terrorism, pilot error, mechanical failure, an electrical fire, or an Act of God, such as a lightning strike? (In other words, what is your initial guess about what may have happened?) For simplification, let’s assume that all possible guesses fall into one of two broad categories: “fair” or “foul”; further assume equal prior probabilities for both scenarios: fair = foul = 0.5.
(Note #2: the “fair” category refers to the possibility of a non-intentional accident, such as mechanical failure, pilot error, an Act of God, etc., while the “foul” category refers to the possibility of some form of intentional foul play or crime.)
Now, starting with 50/50 fair or foul priors, in what direction would you “update” or revise your priors in light of all the new pieces of evidence that have emerged since the aircraft’s initial disappearance? That is, are you willing to tentatively modify your initial guess towards the “fair” direction or towards “foul”? By way of example, consider this mini-Bayesian chronology of the evidence regarding the fate of Flight 370:
Time T1. On day one (8 March 2014) we learned that Flight 370 did not reach its pre-programmed destination in Beijing. In other words, something went wrong, but what? (This is why we should assume equal prior probabilities for both fair and foul scenarios–both initial guesses are equally likely in the absence of any additional information.)
Time T2. Soon thereafter, we learned that the flight transponders aboard the aircraft were shut down mid-flight. (Fair or foul? That is, given this piece of evidence, in which direction should we update our priors?)
Time T3. Later, we learned that the flight path of the aircraft deviated from its original route. The Boeing 777 made a sharp turn mid-flight towards the Indian Ocean. (Fair or foul?)
Time T4. We then learned that the aircraft may have reached an abnormal altitude of 45,000 feet, a very dangerous altitude, and that the aircraft continued to fly for another four to five hours after it changed course. (Again, fair or foul?)
Time T5. About a week after the plane’s initial disappearance, we learned that the Captain of the doomed flight had a flight simulator in his home. (Same question as above.)
Time T6. Yesterday, we learned that the First Officer’s last words to Air Traffic Control (“All right, good night”) were uttered 12 minutes after the plane had deviated from its original flight path. (Ditto.)
Time T7. And today we learned some computer files were deleted from the Captain’s flight simulator. (Ditto.)
Although this Bayesian chronology contains just a small sub-set of all the evidence in this case, our larger point is this: what were your priors when you started (e.g., were they 50/50?), and more importantly, have you updated or revised your priors in light of all this new information, or are you sticking to your priors, to your initial guess, no matter what?