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Assuming you don't find the object in that location, you can update the probability of finding that object by iteratively updating the probability with Bayes theorem.To make this concrete, suppose we have a particle in a 2D box.Let the box be 61 units by 61 units wide and divided into 3721 “cells” of 1 square unit.When looking for objects in difficult places, such as under water or in rough terrain, it may be very difficult to find an object even if it exists.Bayesian search theory starts by by expressing the probability that an object \( O \) will be found in a location \( (x, y) \) is as by the product \( P(O) \) and \( P(D | O) \) where \( D \) is the event of detection of the object \( O \). For instance, the probability of me finding a scarp of paper is smaller in my office which is overflowing with scraps of paper than in my kitchen despite the fact that my office is much more likely to contain the scrap of paper.To use Bayesian search theory to find an object, you would calculate the probability that the object will be found in each location on the basis of the detection probability and the prior probability.You would then search first in the location most likely to result in you successfully finding the object.
The Navy started a search using Bayesian search theory.
Bayesian search theory recognizes that there are two factors that contribute to the probability of finding a lost item in a given location: the probability that the object is in a given location and the probability of locating the object given that it is in the searched location.
The US had a pretty big problem on their hands in 1966.
Two planes had hit each other during a in-flight refueling and crashed.
Normally, this would be an unfortunate thing and terrible for the families of those involved in the crash but otherwise fairly limited in importance.