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04:46
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Crash Course: Statistics
Bayesian Search Theory
04:46 - 07:19
Explains how Bayesian Search Theory was used to locate military submarines.
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Video Transcript
4:45
millions of lives.
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In WWII, German U-boats were systematically taking down Allied ships, including unarmed
4:52
merchant ships with supplies.
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While some ships escaped unharmed like the Empress of Scotland which carried Turing from
4:59
New York back to Europe the Allied forces suffered many losses.
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Locating the U-boats was not an easy task, but the mathematician B.O.
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Koopman used Bayesian reasoning.
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Koopman would first ask experts where the U-boat was likely headed.
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With limited time and resources, prior information and beliefs about the U-boat were important.
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Koopman commented that: “Police will patrol localities of high incidence of crime.
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Public health officials will have ideas in advance of the likely sources of infection
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and will examine them first.”
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And he wanted to do the same with the German U-boats.
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Using signals from the ship, Koopman was able to target a 236 mile radius for planes to
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search.
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But that’s still big.
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He would assign a 50-50 probability that the U-boat was inside the circle, then he would
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use all of the military information that he had access to in order to update those beliefs.
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That way he could make the best decisions with whatever information he currently had.
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Think about the last time you lost your keys.
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You could plot out a grid that represented your apartment, and you could assign a probability
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that your keys are in each 1 foot by 1 foot square based on the likelihood of possible
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ways you misplaced them.
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So maybe your keys fell out of your bag, which would put them somewhere in this square.
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Or maybe your cat got into your bag and dumped its contents onto the floor.
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Then they’d be in this square.
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Or maybe you left them in your jacket pocket.
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Then they’d be here.
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Based on how likely you think these scenarios are...and the knowledge that your cat loves
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to push things off of tables... the best guess is that the cat knocked over your bag again...you
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can use Bayesian reasoning to create a probability map of where your keys are most likely to
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be.
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You could also include information about how likely you are to find your keys if you searched
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for them in that square.
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Keys that fell behind the refrigerator might be hard to find even if you did search there.
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It’d also be really hard to find your keys if they went down a drain outside your door.
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Combining all this information would leave you with a map of your apartment that tells
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you the best places to search.
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This same theory--called Bayesian Search Theory-- was also applied by John Craven to find a
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missing nuclear submarine in 1968.
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Craven collected experts’ opinions on what happened to the USS Scorpion, and used Bayesian
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Search Theory to create a map of where the sub would likely be found.
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And it worked! Craven found the sub right next to where he expected it.
