Using Bayesian Analysis to find a lost nuclear weapon

Ten years ago I picked this book up at an airport bookstore, Blind Man's Bluff: The Untold Story of American Submarine Espionage, by Sherry Sontag and Christopher Drew. Some thinking I've been doing recently related to a project reminded me of this example of Bayesian Analysis described in the book:

[In January, 1966] A B-52 bomber had collided with an air tanker during a refueling operation 30,000 feet in the air off the coast of Palomares, Spain, losing its atomic payload. Three of the four bombs were recovered almost immediately. But a fourth was lost and had presumably fallen to the bottom of the Mediterranean.

[...]

[Naval intelligence officer John P.] Craven called in a group of mathematicians and set them to work constructing a map of the sea bottom outside Palomeres.

[...]

Once the map was completed, Craven asked a group of submarine and salvage experts to place Las Vegas-style bets on the probability of each of the different scenarios that might describe the bomb's loss being considered by the search team in Spain. Each scenario left the weapon in a different location.

Then, each possible location was run through a formula that was based on the odds created by the betting round. The locations were then replotted, yards or miles away from where logic and acoustic science alone would place them.

[...]

[Craven] was relying on Bayes' theorem

[...]

Craven applied that doctrine to the search. The bomb had been hitched to two parachutes. He took bets on whether both had opened, or one, or none. He went through the same exercise over each possible detail of the crash. His team of mathematicians wrote out possible endings to the crash story and took bets on which they believed most. After the betting rounds were over, they used the odds they created to assign probability quotients to several possible locations. Then they mapped those probabilities and came up with the most probably site and several other possible ones.

Without ever having gone to sea, the team now believed they knew where the bomb was [...] in a deep ravine [far from where the first three bombs were recovered].

Long story short, a deep sea submersible found the bomb in that ravine, right where the calculations plotted it would be.

Zen and the art of portfolio management

John Hussman's latest market commentary is replete with Zen koans, quotes from a Vietnamese Buddhist monk (Thich Nhat Hanh, pictured above), plus some thoughts on expected return probabilities. You may need to get up and stretch about half way through to stay focused, but it's an interesting read.

Hussman's Latest

In In his latest market commentary, "Comfortable with Uncertainty", Dr. Hussman shares some thoughts on dealing with market uncertainty, describes a new autism-related discovery by the Miami Institute for Human Genomics (with which Hussman is involved via his eponymous foundation), mentions that he was the subject of a Money magazine profile (though doesn't link to the article), and throws in a little self-deprecating humor to boot. A few brief excerpts:

On dealing with uncertainty:

In his book On Being Certain, neurologist Robert A. Burton quotes F. Scott Fitzgerald – “The test of a first rate intelligence is the ability to hold two opposed ideas in the mind at the same time and still retain the ability to function.” Buddhist teacher Pema Chodron calls it “being comfortable with uncertainty” – being willing to take every aspect of reality as the starting point, without wasting energy wishing things were different, without denying reality as it is (even if your next step is to work toward changing things), and without needing to know what will happen in the future. “The truth you believe and cling to makes you unavailable to hear anything new. The best thing we can do for ourselves is to be open to an unknown future.”

Burton offers the same advice. Tolerating the unpleasantness of uncertainty, he writes, “is the only practical alternative to cognitive dissonance, where one set of values overrides otherwise convincing contrary evidence. Each position has its own risks and rewards; both need to be considered and balanced within the overarching mandate: Above all, do no harm. Science has given us the language and tools of probabilities. We have methods for analyzing and ranking opinion according to their likelihood of correctness. That is enough. We do not need and cannot afford the catastrophes born out of a belief in certainty.”

Hussman humor:

See, I really can write a whole weekly comment without repeating that the bondholders of mismanaged financial companies should be required to accept debt-for-equity swaps or haircuts, with the alternative being government receivership. Didn't even mention it.

Oops.

The photo of Hussman above, by Nigel Parry, accompanied the Money article ("Best Bear Market Fund Manager Around") to which Dr. Hussman (perhaps in his excitement about the autism discovery) apparently forgot to include a link in today's market commentary.