False alarm curve for envelope of Gaussian random field

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False alarm curve for envelope of Gaussian random field

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© British Crown Copyright
Published

Tractable expressions for the probability that the global maximum of the envelope of a Gaussian random field exceeds an arbitrary threshold are provided; this probability is shown to be completely insensitive to the fine details of the correlation function of the random field. The validity of the results is assessed by comparison with computer simulation, where excellent agreement is obtained.

Inspec keywords: probability; signal detection; correlation theory; Gaussian noise; matched filters

Other keywords: matched filter; signal detection; arbitrary threshold; false alarm curve; envelope; global maximum; probability; correlation function; Gaussian random field

Subjects: Signal detection; Other topics in statistics; Signal processing theory; Other topics in statistics

References

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      • K.J. Worsley . Local maxima and the expected Euler characteristic of excursion setsof χ2, F and t fields. Adv. Appl. Probab. , 13 - 42
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