On optimal Bayes detection

Technical Report · Mon Aug 12 00:00:00 EDT 1991

OSTI ID:7368551

Nielsen, P ^[1]

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1. Lawrence Livermore National Lab., CA (United States) Arizona Univ., Tucson, AZ (United States). Dept. of Electrical and Computer Engineering

The following is intended to be a short introduction to the design and analysis of a Bayes-optimal detector, and Middleton's Locally Optimum Bayes Detector (LOBD). The relationship between these two detectors is clarified. There are three examples of varying complexity included to illustrate the design of these detectors. The final example illustrates the difficulty involved in choosing the bias function for the LOBD. For the examples, the corrupting noise is Gaussian. This allows for a relatively easy solution to the optimal and the LOBD structures. As will be shown, for Bayes detection, the threshold is determined by the costs associated with making a decision and the a priori probabilities of each hypothesis. The threshold of the test cannot be set by simulation. One will notice that the optimal Bayes detector and the LOBD look very much like the Neyman-Pearson optimal and locally optimal detectors respectively. In the latter cases though, the threshold is set by a constraint on the false alarm probability. Note that this allows the threshold to be set by simulation.

• Research Organization: Lawrence Livermore National Lab., CA (United States)
• Sponsoring Organization: USDOE; USDOE, Washington, DC (United States)
• DOE Contract Number: W-7405-ENG-48
• OSTI ID: 7368551
• Report Number(s): UCRL-ID-108166; ON: DE93014831
• Country of Publication: United States
• Language: English

Related Subjects

47 OTHER INSTRUMENTATION
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
DETECTION
STATISTICAL MODELS
SIGNAL CONDITIONING
MEASURING INSTRUMENTS
NOISE
PERFORMANCE
PROBABILITY
STOCHASTIC PROCESSES
MATHEMATICAL MODELS
440800* - Miscellaneous Instrumentation- (1990-)
990200 - Mathematics & Computers