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.
Experienced submarine commanders were interviewed to construct hypotheses about what could have caused the loss of Scorpion.
At the end of October 1968, the Navy's oceanographic research ship, Mizar, located sections of the hull of Scorpion on the seabed, about 740 km (400 nmi; 460 mi) southwest of the Azores,[5] under more than 3,000 m (9,800 ft) of water.
The court of inquiry was subsequently reconvened and other vessels, including the bathyscaphe Trieste II, were dispatched to the scene, collecting many pictures and other data.
Although Craven received much credit for locating the wreckage of Scorpion, Gordon Hamilton, an acoustics expert who pioneered the use of hydroacoustics to pinpoint Polaris missile splashdown locations, was instrumental in defining a compact "search box" wherein the wreck was ultimately found.
Hamilton had established a listening station in the Canary Islands that obtained a clear signal of what some scientists believe was the noise of the vessel's pressure hull imploding as she passed crush depth.
A Naval Research Laboratory scientist named Chester "Buck" Buchanan, using a towed camera sled of his own design aboard Mizar, finally located Scorpion.
[5] The towed camera sled, which was fabricated by J. L. "Jac" Hamm of Naval Research Laboratory's Engineering Services Division, is housed in the National Museum of the United States Navy.
The classical book on this subject The Theory of Optimal Search (Operations Research Society of America, 1975) by Lawrence D. Stone of Metron Inc. won the 1975 Lanchester Prize by the American Operations Research Society.
They know the a priori probabilities at the beginning and update them by Bayes' law after each (unsuccessful) attempt.