How to search for a lost object

The joke goes, that a drunk searches for lost keys right under the street lightning, because there its easier. But how would a mathematican do it?


John Pina Craven found a lost nuclear bomb  in deep sea.
The method he applied was Bayesian search theory.
In 1866 a US B52 bomber exploded over Spain:

The aircraft and hydrogen bombs fell to earth near the fishing village of Palomares. [...] Three of the weapons were located on land within 24 hours of the accident—two had exploded on impact, spreading contaminated material while a third was found relatively intact in a riverbed. The fourth weapon could not be found despite an intensive search of the area—the only part that was recovered was the parachute tail plate, leading searchers to postulate that the weapon's parachute had deployed, and that the wind had carried it out to sea.

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. Orts was contacted by the U.S. Air Force to assist in the search operation.

The method applied in one of the four areas identified as probable target [i]