before the start of searching, one can say, hypothetically, "there is a 65% chance of finding it in a 5-day search. That probability will rise to 90% after a 10-day search and 97% after 15 days" or a similar statement. Thus the economic viability of the search can be estimated before committing resources to a search. Apart from the USS Scorpion, other vessels located by Bayesian search theory include the MV Derbyshire, the largest British vessel ever lost at sea, and the SS Central America. It also proved successful in the search for a lost hydrogen bomb following the 1966 Palomares B-52 crash in Spain, and the recovery in the Atlantic Ocean of the crashed Air France Flight 447. Bayesian search theory is incorporated into the CASP (Computer Assisted Search Program) mission planning software used by the United States Coast Guard for search and rescue. This program was later adapted for inland search by adding terrain and ground cover factors for use by the United States Air Force and Civil Air Patrol. Mathematics Suppose a grid square has a probability p of containing the wreck and that the probability of successfully detecting the wreck if it is there is q. If the square is searched and no wreck is found, then, by Bayes' theorem, the revised probability of the wreck being in the square is given by For every other grid square, if its prior probability is r, its posterior probability is given by USS Scorpion In May 1968, the U.S. Navy's nuclear submarine USS Scorpion (SSN-589) failed to arrive as expected at her home port of Norfolk, Virginia. The command officers of the U.S. Navy were nearly certain that the vessel had been lost off the Eastern Seaboard, but an extensive search there failed to discover the remains of Scorpion. Then, a Navy deep-water expert, John P. Craven, suggested that Scorpion had sunk elsewhere. Craven organised a search southwest of the Azores based on a controversial approximate triangulation by hydrophones. He was allocated only a single ship, Mizar, and he took advice from Metron Inc., a firm of consultant mathematicians in order to maximise his resources. A Bayesian search methodology was adopted. Experienced submarine commanders were interviewed to construct hypotheses about what could have caused the loss of Scorpion. The sea area was divided up into grid squares and a probability assigned to each square, under each of the