Wednesday, 28 April 2010

Bayesian Bomb

Bayes' theorem

In probability theory, Bayes' theorem shows the relation between one conditional probability and its inverse; for example, the probability of a hypothesis given observed evidence and the probability of that evidence given the hypothesis.

It is named for Rev. Thomas Bayes (pronounced /bejz/) and often called Bayes' law or Bayes' rule.

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1966 Palomares B-52 crash

The Palomares Incident or 1966 Palomares B-52 crash occurred on January 17, 1966, when a B-52G bomber of the USAF Strategic Air Command collided with a KC-135 tanker during mid-air refuelling at 31,000 feet (9,450 m) over the Mediterranean Sea, off the coast of Spain. The KC-135 was completely destroyed when its fuel load ignited, killing all four crew members. The B-52G broke apart, killing three of the seven crew members aboard.

Of the four Mk28 type hydrogen bombs the B-52G carried, three were found on land near the small fishing village of Palomares in the municipality of Cuevas del Almanzora, Almería, Spain. The non-nuclear explosives in two of the weapons detonated upon impacting the ground, resulting in the contamination of a 2-square-kilometer (490-acre) (0.78 square mile) area by radioactive plutonium (akin to a dirty bomb explosion). The fourth, which fell into the Mediterranean Sea, was recovered intact after a 2½ month-long search.

The search for the fourth bomb was carried out by means of a novel mathematical method, Bayesian search theory, led by Dr. John Craven. This method assigns probabilities to individual map grid squares, then updates these as the search progresses. Initial probability input is required for the grid squares, and these probabilities made use of the fact that a local fisherman, Francisco Simó Orts,popularly known since then as "Paco el de la bomba" ("Bomb Frankie"), witnessed the bomb entering the water at a certain location.

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