Underwater Acoustics (Analysis, Design and Performance of Sonar) || Statistical Detection Theory

✍ Scribed by Hodges, Richard P.

• Book ID: 102682485
• Publisher: John Wiley & Sons, Ltd
• Year: 2010
• Tongue: English
• Weight: 598 KB
• Edition: 1
• Category: Article
• ISBN: 0470688750
• DOI: 10.1002/9780470665244.ch12

✦ Synopsis

Statistical Detection Theory

Detection theory is applying statistics to the decision process. Take the problem of detecting if a coin is biased. To do this, we would perform an experiment and measure how often heads came up and compare that to what a fair coin could be expected to do. Suppose the coin was flipped three times and it came up tails all three times. We could not say with 90 % confidence that the coin is biased because one time in eight, three tails will come up from the flips of a fair coin. Suppose the coin came up tails 50 times in a row, any reasonable person would conclude that the coin or the tossing procedure was biased since this would only come up one time in two to the fiftieth (1 in 1120 trillion) with a fair process. With some forethought, an experiment can be designed to do this in a less arbitrary manner. By confining our decisions to two outcomes or hypotheses, biased or not (signal present or not), the problem becomes a binary decision. This same technique can be applied to an m-ary process as well, e.g., if we were trying to detect a set of bits that were to represent the alphabet.