Detection theory

Detection theory or signal detection theory is a means to quantify the ability to discern between informative signals in an otherwise noisy environment. Its applications are broad, ranging from radar and sonar to medicine, psychology, and data science.

Overview

Detection theory was developed during World War II for the analysis of radar signals. The theory has since been applied to a wide variety of areas, including sensory neuroscience, diagnostic medicine, and data science.

The fundamental problem addressed by detection theory is distinguishing between signals and noise. In the context of detection theory, "signal" refers to the pattern of interest, while "noise" refers to other patterns that might interfere with the signal.

Mathematical Formulation

The mathematical formulation of detection theory is based on probability theory and statistics. The key concept is the likelihood ratio, which is the ratio of the probability of observing a particular outcome if the signal is present to the probability of observing that outcome if the signal is not present.

Applications

Detection theory has a wide range of applications. In radar and sonar, it is used to distinguish between signals reflected off an object and background noise. In medicine, it is used to determine whether a particular pattern in a patient's symptoms indicates a specific disease. In psychology, it is used to study perception and decision-making. In data science, it is used to detect patterns in large datasets.

See Also

• Probability theory
• Statistics
• Radar
• Sonar
• Medicine
• Psychology
• Data science

References

• Peterson, C. A., Birdsall, T. G., & Fox, W. C. (1954). The theory of signal detectability. Transactions of the IRE Professional Group on Information Theory, 4(4), 171-212.
• Green, D. M., & Swets, J. A. (1966). Signal detection theory and psychophysics. New york: Wiley.